The sleeve puller I made for the ammonia compressors at work consisted very much of what you have there. The only difference was the bottom part. I made a 1/2" flat plate just a tiny bit smaller in diameter than the sleeve itself, with two flats ground on the sides so I could put it in from the top, then turn it into position and thread the rod into it - there wasn't much room to work from below is the reason I did it this way.......if this sleeve is "sticking", I'd knock it back down and look for the reason, maybe you're puller is hanging up on something from below, or it's causing the sleeve to cock in the bore?
You're design is OK, but I might have drilled holes where the studs are so the crossbar could "float" a bit and used pieces of pipe to support the crossbar instead of pushing down on the head bolts - if that's what I'm seeing in your pics...........