Wild pigeons aside, I think you are on the right track. I have 2 hand-fed, hand-tamed budgies. The male is much more affectionate & also talks. The female is, well, a b*&ch. But that's who she is, so I work with it.
The thing with budgies (and I've got bigger parrots, so have the same level-of-comparison you do), the budgies like people who pay them attention. The males are easier to 'tame' than the females. Yours doesn't have a girlfriend, so will be looking for attention & that gives you something to use.
And in general, the budgies don't realize they are little birds. My male budgie will challenge my Pionus for his food on a daily basis. I think the budgie thinks he is a macaw (who got hit by a shrink ray).
They are also copycats. So the budgie will make note of the good interactions he sees between you & the bigger birds & when he is comfortable with you, will try to get the same reactions the big birds get. Make him jealous of your relationship with the macaw & the grey & you'll get a lot of good results.
Enjoy.
We have 1 Yellow Nape Amazon, 1 Congo African Grey, 1 White Capped Pionus, a bonded pair of Liniolated Parakeets & 1 pair of budgies. Every single bird in this mixed flock has learned at least one thing from each of the other birds. Budgies are smart little guys. You'll be amazed at the relationship you can develop with yours.
They were surprisingly easy to tame and it made them sell WAY quicker. I always selected males for this as well, for some reason they always seemed much friendlier than the girls.
