Congrats on the .35 Whelen! Although, personally, I wouldn't have given up a Rem 600 6mm for it (I'm a bit odd, that way) unless I had a couple duplicates!
In fact, that's how I got my 6mm, I traded one of my "spare" M600 .308s for it.
As to the cock on closing M600 you had, I think either you were just mistaken, or it was a one of a kind custom job, and your description of the rest of the rifle casts that in serious doubt.
Cock on closing would have required a large change to the cocking mechanism (internally) and I have never heard of Remington doing any like that with any of their bolt guns.
The basic design of the modern Remington bolt (cocking group) goes back to the Models 721/722 bolt guns from the 50s. Model 600 & 700 (all types) use it also. They are all based on the same action design (roughly). The 788 guns are a completely different action.
I'm not saying you didn't see what you saw, it just seems to me unlikely. One thing I have learned in nearly 50 years of gun collecting (ok, aquiring mostly) is never say never...
For those reading this that aren't quite sure what I'm talking about, the way it works is this:
A cock on closing gun moves the striker assy (firing pin, cocking piece, etc) back slightly when you lift the bolt handle. You pull the bolt back. As you push it back closed, at a point shortly before the bolt is fully shut (not locked) the cocking piece catches on the sear, and is held there as you push the bolt shut against spring pressure. Turning the bolt down, locking the action will move the bolt all the way forward, while the cocking piece is held where it is.
A cock on closing gun will move the cocking piece most of the way back, and will be held there by the bolt as you lift the bolt handle. Close the bolt, and the striker contact is tranferred from the bolt body to the sear. The striker may appear to move back slightly when locking the bolt closed.
This varies from specific action to action design (along with how well you can see it), but the basic difference is that most, or all, of the force needed to compress the firing pin spring is done when you lift the bolt handle on a cock on opening action. That same force is exerted when you close a cock on closing action.
The striker of a cock on opening gun may move backwards slightly when locking the bolt down (depending on the design), but nearly all of its movement is done when opening the bolt. The cock on closing gun moves the striker just a little when opened, and the rest of the "movement" is on closing. (in most designs, it is bolt body movement, the striker is held in place)
Clear as mud now?
ITs really easy to see if you can look at the two types side by side. Sadly, while I have examples, I can't show you here. Take a 98 Mauser and an SMLE (or a 95 mauser) and look, its easy to see the difference. Sporting rifles can be more subtle, but its still easy to see, if you know what you're looking for.