The 35 Whelen it is a great round whitetails right on through moose, especially in Canadian shield country where shots are rarely over 250 yards. Unfortunately your choices of rifles that are readily chambered for it are limited. My 35W is a Remington 700 CDL and I like most things about it other than the annoying hinge floor plate. In hindsight I would have bought a CZ in 9.3x62. Not so much for the difference of the round (minimal), but for the better overall quality of CZ and a detachable magazine.
My CZ 9.3 X 62 does NOT have a detachable magazine, and it was my understanding that only the short cartridges were DM'd in the 550, have I been misinformed?
To the OP, what is it about the Rem stocks that is not fitting properly? Are you of small stature and small hands?
Don't listen to all the anti-Rem hype on this forum, I've owned more than 100 Rems over the years and have more than 30 in my vault right now. There are some problems over the years but I've yet to see one that wasn't easily corrected. I've successfully hunted African dangerous game with a 700 Rem in .375 and hunted over a lot of the world with another old Rem in 300 Wby and have yet to have a Rem let me down in the field with tested and proven loads.
If the Rem stock doesn't fit you the CZ I suspect would be even worse as it is thicker through the grip and LOP seems a touch longer, on the 2 that I have, than the Rem stocks.
If you like I have a Rem 35 Whelen take off bbl I would sell and all you need to do is check with a smith as to thread and shank dimensions (sorry not familiar with stevens at all)
You didn't indicate your preferance as to stocks, wood or other. I would suggest, as have many before , buy a Rem 700 used in a classic or CDL and have the stock modified to fit as this should be less expensive than re-bbling the stevens and you will end up with a better firearm. If you want synthetic then it's a no-brainer, go with the 700 Rem and do to the stock whatever you need to to make it fit, a replacement 700 synthetic stock is $99.00
Just my humble opinion.