It’s natural for an animal to not want to move when they are laying comfortably somewhere. Have you done all you could to make the crate a positive experience? Robert has good videos on that and you could start at anytime. Anytime my dog goes in the crate, he gets a reward – anything from a kong stuffed w/ frozen raw turkey to a few pieces of kibble – always something though. He’s not stoked on the crate but he’s also ok with it – he knows at least something good will always happen when he goes in there.
Don’t think about how to “win” when he starts acting like – think about how to set things up so he never acts like that in the first place. If you need him to move him, can you use a treat to lure him? What about working on a recall?