my fiance and I are having similar problems with our gelding. Since before we got him, we were told he was worked with every day to pick up his hooves and they had little success. Since we moved him, i've been able to work with him more and for a longer time period.
Gem doesn't have a problem when you pick up his back feet, he could stand there all day, but with his front feet, he'll let you pick it up and then he'll lean back to where you have to let him put his foot down or else his bum is going to touch the floor.
I have backed up into a corner and when he does this, his bum will hit the walls and i can pick his feet. But, i found that if you hang on for dear life, he'll be ok, but if you try to pick it up again, he won't have it.
So what i did was let him have his foot whenever he wants it (he is also lame and has arthritis so i don't know if what i do will work for you and spree) But when i take his foot back up, i hold it for one second longer than before, until it's all cleaned out. I do that for 2 of his feet and then take him out for grass, as a reward for letting me clean his feet.
His left side is better to pick up than his right. With his right front, he'll lean into you and will move all other feet, but that one. So i have done everything to that leg BUT pick it up. I'll massage it, clean the outside of his hoof, pet his leg, brush his leg to take his mind off it. I'm not sure if its more for him, or more of a way for me to relax. But when i try and pick it up again, he'll usually let me. And then if he needs his foot back, i'll give it to him (as long as it's not a pick up and immediately he puts it down) Then when his front his done, i move to his back and then out to grass we go.
I do this in his stall as he doesn't like to be restricted, and then i feel he has the ability to find a place that is comfy for him.
I have been working with Gem for the past 2 days consistantly and i think we are getting somewhere. Just remember to be patient and if you're getting frustrated, do something else :) and when you're ready to continue, continue. If there is something Spree likes, eating grass, or getting her favorite treat, try and see if rewarding her for letting you pick her feet helps you any. If you're not into giving treats, a good scratch would be good too!
I hope i have helped some :)