Johnnyote, when I used to be able to use lead bullets out of my old 22-250 I killed a bunch of coyotes with Sierra 55 gr BTHP bullets and the Hornady 55 gr V-Max bullets and never had a splash or large entry hole. These bullets were loaded pretty close to maximum loads and I didn't get very many exit holes on coyotes.
In the 22-250 you may be better off loading a tougher, heavier bullet with a higher BC so you will have a nice 22-250 load.
I just looked in my Barnes Reloading Manual Number 4 and the slowest minimum load for their 36 gr Varmint Grenade in the 22-250 is over 3826 fps, all the other minimum loads were over 3932fps with one minimum load at 4002 fps.
If you use a 55 gr lead bullet with a much higher BC and load it at a medium load around 3400 fps to 3500 fps you may do less damage than a lightweight varmint bullet doing 3800 fps.
If you want to shoot 35 gr bullets you really don't need a 22-250, you can shoot 35 gr bullets over 4000 fps out of a 223 Rem.
The best Lead Free bullet I have used so far on coyotes out of my 1-8" twist 22-250 and RRA AR-15 Upper with 1-8" twist has been the Barnes 55 gr MPG bullet.