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.
You can also add Sierra's bullet #1365 to the list. It is a 55 gr Spitzer that holds together well. I have no experience taking deer sized game with a .22 nor would I want to.
This bullet will handle the velocity. I have run it to 4150 fps in my .22-.243 Middlestead. On coyotes the exit wound is about the size of two fingers. I have shot coyotes running away at distances under 200 yards where the bullet enters somewhere near the "Bulls-eye" and exits the chest/neck area.
My brother played around with the Barnes X 53 gr in a .22-.250 Ackley at 3950 fps to shoot coyotes this year. Entry was very small and exit was about the size of a index or pointer finger that we all wish our proctologists had.
To manufacture a solid copper bullet for a 22 caliber in the 85 to 100gr range would require a very fast twist to stabilize. Since copper is about 15% less weight, by volume, then lead, the copper bullet would be much longer in the 85gr then a lead filled bullet. At this time I have no plans on developing a 22 caliber bullet. As always customer feedback will determine what calibers I introduce. So, I won't say never.
I have a 243 bullet in the works. The 243 may be an option for a young hunter. The recoil of a 243 is minimal.
As to having deer run off using my 22, no, I have not had any deer run off. I wait until I have "the" shot before I shoot - broadside. I have never had one exit on a deer. It "seems" that once the 52gr bullet enters the lung area it explodes and makes a real mess of the lungs. It turns them off pretty fast.
For high velocity chest impacts I use the 55gr. FMJ-BT. I shoot them at 4260fps with great accuracy. And yes they will expand! I think what actually happens with this bullet is that it flips over and expands from the back because the jacket does not cover the lead on the back.
I have not had good results with getting accuracy out the barns bullets but everyone I talk to says they kill deer really well.
The 55gr. sierra BTSP also works good on deer, I watched my buddy shoot one in the lungs with impact velocity of 3200fps and only left a small exit hole not sure about higher velocity though, the deer took three steps and tipped over.
I have used the Hornady 55gr vmax -the Hornady 52grmatch-52gr Amax-68gr match-75gr match with all having devastating effect with neck and head shots!! I am particularly stuck on the 68 gr match but I have a 1/9 twist rate. If you have less twist the lighter bullets will work great. The only thing about the vmax bullets is that you cannot take a shoulder shot aiming for the bone. I have gotten a lot of friends to try the Hornady offerings and they are stuck so I would say if you try them you will like them too!!