Yes, move it slowly into his area and adding his favorite treats all help.
However, most travel cages are more commonly used to transport the Parrot from Home to the Avian Vets office and back. And, the only time that 'thing' shows up is when its time to make that trip! So, the travel cage rarely is associated with anything good. Well with the exception of the trip home from the Vets. Yup, rarely a problem getting them back in the travel cage in the Vets office.
Now, several members use a more open travel 'backpack' like carrier and that's commonly used for 'fun' trips. Guess, which one the Parrots more easily climb into: Yup! The one that is associated with 'fun' trips.
But your problem is more the fact that it is 'new' and has not yet developed a reputation. In addition to it being 'new,' these things commonly show-up and are pressed into service. So, your emotions of needing to get the Parrot into, and the quicker the better, will work against you.
At some point you will just need to get the Parrot into the Travel Cage. Yes, do all the things regarding exposure to, and treat and toy hiding place, etc... However, it may just not get to a point of the Parrot believing its a place he wants to get into.
So, onto the push the Parrot into the thing! Its not like we Parrot people are the only ones with this problem. I have watched Cat people pour their cat into these things and the same with Dog people. They all have biting and scratching tools, but Parrots have Wings! This requires that the Parrots head is heading first into the travel cage with your free hand slightly covering but not holding the Parrots body /wings. Too a certain degree its like a quick, near the cage and to into the cage movement. Rarely pretty, not always successful, sometimes painful (bite), but it does work.
The hard plastic small animal (also know as Cat Carrier) is a better choice because the two piece construction allows one to easily add a perch near the door. The perch is a known thing and helps the Parrot since stepping onto a perch is a known action.