Is there a way to convert the Park PCS-12 to PCS-10?
You're not going to be able to buy just the floor stand without the clamp unless you chance to buy one at a yard sale or on ebay, you might be able to contact Park Tool and ask them if they can send you just the floor stand without the clamp as a replacement part, but I doubt it for that particular stand. 

My advice would be to just buy the new stand, amazon sells them for $90 less than their listed price. And you can get them for even cheaper than that on ebay. Then you can keep you bench mount for spare parts or just leave it where it is and have two stands.

You could try building a floor stand out of chain link fence parts depending on the size of post you need to fit the clamp. The cheapest solution would probably be to buy one post (or borrow one from a local school) and a floor flange, and either bolt it to your garage floor (permanent) or to a big piece of thick plywood (which will eventually break). I don't recommend looking at getting piece of plate steel like the PRS Deluxe stands have, because I've looked into it before and the size plate you's want would cost almost as much as a new PCS stand would. If you can get anything free by chance or from a junker/someone you know then that's a bonus.

But like I said, I think you'd be better of just to buy a new stand.