Say I had a Winchester Classic Super Grade in 30-06. What would be the pros and cons of rebarreling this rifle, with the 06 action length, to .358win?

The .358 Winchester is just right for a short action rifle. If you already have a long action you might as well fill it up with a long action cartridge. Thus the .35 Whelan or .35 Whelan Improved would be logical.

Of course the orginal M-70 chambering was in a action that while it had a short stroke was long enough for a .375 H&H!

The path of least resistance is just to order a .35 Whelan in whatever rifle suits you.

If you just want a .35 caliber rifle then that would be reasonable but no real step-up from an '06. A .35 whelen would be a sizable step-up from '06.