I worked up a load for Barnes 210 gr bullets in my 375 H&H (but mine is a Remington 700 Classic-still very a light 375 H&H). It kicks less than the Remington Factory 260? gr (I can't remember, it's not the 300gr, it's the regular Remington Core Lokt I shoot in it). I did it just for deer. But I'm changing my mind as I don't want two loads and the Core Lokt shoots really well and doesn't kick much more. Not sure how it would be in an Encore.
I about with some of the other posters, 35 Whelen is pretty darn nice. I might would spring for a 9.3x62 as it's a little more than 35 Whelen. But 375 H&H you can take just about any kind of hunting in North America if you ever had the chance.
If you are going to handload, I don't see why not use a 375 H&H, you can download it pretty far (using the correct powder, follwing load manuals of course). I tried that using 220 gr Hornady FP's (for the 375 Winchester), but it shot soo much lower than the Factory or 210gr full power load, I decided not to do it.
If you want easily available factory ammo, 35 Whelen is going to be it. There's 35 Whelen Ackley Improved too.
JW