Split the difference... 338-06?
35 Whelen has reputation for recoil. I never fired one. However, I did own a 358 Winchester and currently own a 338 Federal. Each based on the 308 Winchester case.
I can't say they I notice a recoil difference.
Reloading adds another dimension to the issue. You can easily load the 35 Whelen to 358 Win levels, but you can't turn the 358 Win into a 35 Whelen.
But the 38 Win does come in a short action.
My father had a similar issue with a 300 Weatherby that was used for several elk hunts in Colorado. Elk hunts found it loaded with Weatherby factory ammo as no reloads can match Weatherby ammo. Velocity, accuracy, or recoil. But for our PA whitetails, it was loaded down to 30-06 level.