I totally agree with Itzjbean, and I'm totally aware of the "Catch-22" this is presenting you...You absolutely cannot just keep him locked-up inside of his cage for a month at a time, that's not fair to him and it's also not healthy for him, but at the same time he's not a tame bird, and this makes "catching" him very difficult...But as Itzjbean said, you DO ALWAYS HAVE A CHOICE, as you are the person and he is the bird...This really is a safety-issue above all else, but it's also an issue of making his life healthy, happy, and fair. And keeping him inside of his cage 24/7 is not an option either.
***And I'm going to say this just because IT HAS TO BE SAID: There is never 100% certainty that your bird will not at some point out of nowhere during the night fly to your bed while you're asleep and fall asleep on you, on the covers, crawl under the covers, etc., and then you'll roll-over onto him during your sleep and kill him....And it doesn't matter that he's not tame, that he doesn't often come near you at all, or that he has never done it before; none of these mean that he won't do it some night. This happens all the time, every day, and is completely out of nowhere...The statement that "I'm not worried about his safety seeing as once he's on his sleeping spot he doesn't move until morning" is a very "famous last-words" kind of statement that has been said by hundreds if not thousands of pet bird owners who have killed their pet birds during the night by rolling-over on them...It just happens. Period. And then as Itzjbean said above, God forbid there is an emergency in your home, like a fire, where you have to collect him quickly and get out of the house, you can't be chasing him around trying to catch him...
I don't know what type of hand-taming/training you did for that month where he never left his cage, but as you found out, hand-taming exercises don't typically go well when the bird is inside of their cage and you are putting your hands inside the cage at the same time. There are a number or theories as to why this is, but overall it typically doesn't work well...or at all. So the fact that you already have a play-stand that he likes is excellent, because that's probably going to be the best place to work with him, away from his cage and out in the open...It's also a place where he can sit to hang-out with you, no matter where you are in your house (assuming it's a portable playstand)...As far as sleeping on the playstand though, it's presenting the same issues, it's not safe for him and you'll not be able to catch him...So he needs to be sleeping inside of a cage, whether that is his "main-cage" that you say he won't go back to at night, but that he seems to like very much once he's inside of it, OR it's a much smaller "sleeping-cage" that you locate in your bedroom, and that contains nothing at all inside of it except for a perch and a water-dish, and maybe a swing if he likes to sit on/sleep on swings, and that's it, and that you start to associate with bedtime for him. No toys, no food dish, nothing else at all so that they know it's just to sleep in (although if he likes millet-sprays or some other type of specific treat you can hang that/put that inside of the sleeping-cage for him, which usually will make their sleeping-cage a place that they associate with good things and can help to get them to willingly go into it whenever you give them the verbal-cue to do so, something like "It's bedtime! Time to go to your sleepy-cage and get your treat!", and that hopefully they learn is their cue/command to go inside their sleeping-cage to get their bedtime-treat)...This works great for a lot of people, so it's something that is definitely worth trying for sure...And again, for a Green Cheek Conure, a sleeping-cage can be very small and simple, like the typical smaller cage that is meant for Budgies to be housed-in, and that you can either find on your local Craigslist for very cheap, or you can buy new in most pet-stores for $20-$30...So definitely worth a try at least...
***The other thing that you might want to think about, and this won't be a popular suggestion but it's one that works wonders for people in your specific situation, is having his wings-clipped temporarily, with a very conservative clip of ONLY the outermost 5-6 Primary Flight-Feathers on BOTH wings, that will give you about 2-months or so until his wings grow back-in again fully and he can fly again, for you to take full advantage of and work with him one-on-one, every single day of that 2-months or so, so that by the time his wings grow back-in and he can fly again he is regularly stepping-up for you, you no longer have to chase him at all, and also so that he learns to come out of his main-cage on his own whenever you open-up the door, take a step back, and ask him to come out, and then step-up for you once he's outside of his cage, as well as learning to go back inside of his main-cage whenever you ask him to and you take him to it on your finger. And if you do decide to do the sleeping-cage thing, then he should also learn to go inside of it when asked to do so at bedtime to get his bedtime treat, by allowing you to take him to it on your finger....
I don't AT ALL suggest nor condone keeping your bird's wings clipped forever, and not even for longer than the one initial, temporary clipping. And that's not at all what I'm suggesting, as all 4 of my larger birds and all 8 of my Budgies are fully-flighted and have been since they were young babies. However, that being said, when it comes to birds who were not hand-raised/hand-fed or that for whatever reason are afraid of hands, won't step-up after long attempts at training/taming have failed, and who's refusal to step-up for their owners results in them flying away and their owners constantly chasing them and doing other things to gain-control of them that only stresses the bird and the owner, and that only serves to reverse any trust-building that the owner has accomplished, I don't feel that there is anything at all wrong with doing one initial, conservative wing-clipping that gives the owner about 2 or so months where the bird cannot constantly fly-away from them and cause nothing but stress and take away trust. Wing-clipping is completely painless, does no harm to the bird at all, and is completely temporary. And as long as it's not used as a permanent type of "easy training-method" for the lazy bird-owner who doesn't want to put in the daily work during the 2 or so months they can't fly, then there is nothing at all wrong with doing it once...It can actually turn-out to be the difference between a bird and their owner bonding-closely and becoming family who love each other and are always together, and a bird being re-homed/sold over and over and over again...
The idea here is that once your bird's wings are clipped, he won't be able to fly away from you any longer, that's obvious, but in-addition your bird will have to learn to depend on you to get around, which is obviously going to mean that he will have to step-up for you on a regular basis. And for your part, you should be allowing him to come out of his cage whenever you are at home and allow him to be with you, be on you, etc., and what happens is that over the 2-months he cannot fly, he will learn that he can trust you a little more every time he steps-up for you and you take him back to his cage, you take him to his sleeping-cage for his treat, you take him to playstand, you allow him to sit on your shoulder for long periods of time to just hang-out with you, etc. So by the time his wings grow back-in and he can fly again, he'll no-longer be flying away from you, but rather be flying to you whenever you ask him to do so, and just because he wants to...
People will be against doing this, and that's absolutely their opinion, but it's ultimately the decision of each bird's owner, and whenever things get to the point where a bird is no longer being allowed to be outside of their cage because their owners don't want to spend hours chasing them to get back inside, and the quality of life for the bird is going downhill, and any relationship or bond between the owner and their bird is vanishing quickly, my feeling is doing a temporary wing-clipping for 2 months is a much better option than the owner becoming so frustrated with their bird that they re-home them...It doesn't hurt the bird, and only lasts for 2 months, and it typically works extremely well...So why not...