I do not have a parrotlet myself, but do think they are the cutest little things... I fell for one at a petstore and almost purchased him, but being a volunteer at a rescue, I refrained
I do know some of the smaller birds can be very protective of their cage. We have a little green cheek here that will try to chew your arm off if you put your hand in the cage and ask her to step up. Put Victoria worked with her on stick training and she hops right on and once out of the cage is her normal sweet self. I would work on stick training for asking him to step up from the cage. You mention he snuggles up to your neck, is he friendly and nice outside the cage? Or does he get a little flighty with hands in general?
How long as he been with you? Might just need more time to settle in and you two work on your bonding and trust. Try feeding him a treat from your hand while he is in the cage. If he goes for the fingers over the treat, then he may just be protective of his home

If he takes the treat, then you may be dealing more with trust and bonding.
Congrats on the new family member! Post pics, I love the parrotlets, they are so adorable, I'll enjoy him thru you
