Now since the CC's look at purchases & cash differently with VERY different rates, Can I instruct "them" to put the min where ever it is they put it and use the $500 I pay towards the cash balance?

I've had the past experience of seeing the cash balances never going down, of course that's where they make more $$.

If you still have the small print that shows the terms and conditions for use of the card, check there. It will probably tell you how they apply funds received. It may also be listed on your card. In either case, I don't believe you can instruct the company to apply your payment towads the cash advance first. The closest you could come is to transfer the whole balance to another card, where they will not know how the balance was generated.