The Browning BLR, Win 88, and Savage 99 were all made in 358 Winchester at one time or another. The Winchester and Savage are both pretty scarce in that chambering, so price will be accordingly. The Browning BLR is a good rifle and one in 358 winchester can probably still be had for something reasonable.
The re-make Winchester or Browning 1895's were made in 30-06 &/or 270 Win., so a re-barrel to 35 Whelen is certainly possible, but it will require a talented gunsmith and a new barrel. Therefore, that will turn into an expensive project, probably $1500 to $2000 by the time you're done.
If you are not tied to nostalgic old design models, I'd recommend trying to find an older Browning BLR in 358 Winchester. It's not quite the powerhouse of the Whelen, but pretty close. Another idea is to search for a Browning re-make of the Winchester mdl. 71 in 348 Winchester. It's a dandy, and suitable for anything short of the big African stuff. They can still be had for under $1000 and will surely continue to go up in value.
Oh, one other idea. Winchester made a run of Winchester 94 Big Bores in 356 Winchester. The Winchester 356 is a rimmed version of the 358 Winchester. That may be the sleeper, as far as price is concerned.