Birds all have unique personalities just like humans do. They can also get set in their ways
On the food, birds by their nature are suspicious of anything new. So it's very typical that your bird resists anything but seed. Start with lettuce. Clip it to the cage so it's in his face. Eventually he'll start gnawing at it just to get rid of it. The next day, put in more fresh lettuce. Keep at it. Eventually he'll get some into his mouth
. Focus just on lettuce.
It's good that your keet likes his cage, but let's lure him out. He feels safe there - so make a new safe place for him. Make a little playpen next to where you tend to sit. Have millet on it (i.e. parakeet junk food). Only ever give him millet on his playpen. Make sure the playpen is stable and safe feeling. Every day, bring the keet over to the playpen and let him have some millet. Keep that up