Re: 22 caliber bullets
Most of the deer that I have taken with .224 cal have been with .223 and .22-250 so their velocities are slower than the 3500 you are talking. I would suggest the 55 gr. Trophy Bonded bullets or the .22 cal Nosler Partitions if you intend to try for chest shots. Understand that there are other makes coming. Speer used to make a 70 grain .224 bullet that was intended for deer sized critters also, but it was pretty blunt tipped. I killed several deer with it and it was good.
Hit in the chest or preferably the neck, .224 bullets put deer down very well. Have also killed a lot of deer with Matchkings but all shots were in the throat/neck.
Good luck, only one way to find out.