Thank you for your service time
Forget picking his back feet up until you address the greater problem -- the spookines, the goosiness, the kicking and stomping of his feet, the setting back, the threatening of a handler that demonstrates a lack of basic ground training. He is not ready to pick his feet up
^^^This, unless his hooves are so bad he absolutely has to be trimmed; which that doesn't seem to be the case right now.
Work with him every day, if you can. Also, if it's possible I would get him out several times in a day but for short lessons. Whether it's you by yourself, your friend, or both of you, work him several times a day.
As soon as he complies with a request, stop the lessons, do something fun with him that you know he likes, then put him back to pasture or whereever he's kept through the day.
When it's time to mess with his back hooves, this may be up for debate but, for my part, I wouldn't tie him. I would put him someplace safe, like a round pen, big alley way, or anywhere that is sort of confining in case he would get away from you.
I have custom lead ropes that are around 15' long - that gives me plenty of rope to hang the horse or myself (JK
. Really, it gives me enough rope to hold onto it while picking up a back hoof with the other hand, if there's nobody to help.
If the horse wants to dance, I'd let them dance but they did it on three legs; I'm only 5'2" but I wasn't letting go of that hoof until they stopped their Two-Steppin' around. The horse did have some manners by this time and I was reasonably sure it wasn't going to land on top of me.
You sound to be fairly experienced with horses or I wouldn't eeeeeeven mention that method --- it's not something an inexperienced horse owner wants to try as there's a lot of human instinct involved in knowing when to let go or keep holding the leg near the fetlock joint.
I'm glad your friend bought the horse - it sounds like the horse was "kindly abused", if that makes any sense