Re: picking up hooves
My mare is an Irish cob, probably with ID in there as well, has feet like enormous dinner plates, and when we first had her we too struggled with picking her feet up, especially my daughter, who was only 12 at the time !!
She seemed to have difficulty balancing on only 3 feet, so it sounds a bit like yours - we persevered with someone holding her, while another picked up feet, and it did get better over time. Every time she picked up a foot and managed to keep it up, the person holding her made a fuss of her and gave her little treat, if I was there on my own it was a bit more difficult, but I'd do one foot, fuss and treat, then carry on to the next, and so on.
She hadn't had a lot of proper schooling before we bought her, and was somewhat on her forehand, I'm guessing your gelding may be too at the moment - maybe it's to do with their weight distribution?