I had the same problem with Jesse last year. I ended up bending my nice new Oster hoofpick :(. But, from then on I'd use a rasp. I usually just file the ice down until it's thin then I take my hoofpick (99 cents from Princess Auto) and pick it out. As far as the ice balls go, I have the same problem this year. I will usually just use my fingers and hold them until they melt away (for small ones), cut them off, or use a blow dryer.
"You know, for as long as I can remember, I've had memories." ~Colin Mochrie