First off let me tell you welcome to "The City", we're glad to have new members. I suspect the problem may be your 10" orbital buffer. If this is the type of buffer that is purchased at Sears or AutoZone they just don't have sufficient power to do much more than apply a final step product (FSP). Virtually no cutting ability.
There are commercial 10" buffers that are respectable machines, GEM for instance. These however are usually several hundred dollars. The $49, 10" buffer is not what you want to be using for paint correction.
If my assumption here is correct the simple solution is to buy a better buffer. I would suggest looking at a Dual Action (DA) such as the Porter-Cable or Flex XC. These are products that are simple, effective and take much of the risk associated with burn through out of the equation.
The next thing I would suggest is looking at polishes that are Detailer or Commercial quality. Not many of the professional or top enthusiast detailers are going to give you a big thumbs up for the Turtle Wax line of products. If this is the case there is probably a reason why. Many of the OTC products available will work but these manufacturers also takes into consideration the degree of experience the customers that purchase these products possess. These products lean towards the light side (safe) when it comes to cutting ability.
I would suggest you take a look at the PoorBoys series of polishes or perhaps Mothers or Meguiars commercial lines. There is more than one really good polish manufacturer. We also have AutoGeek as a vendor here on this site. They have almost any brand product you can imagine. There are exceptions to what I've written about OTC products here, an example would be the Duragloss line. Virtually every one of their products is worth consideration. Spend some time reading up on products before you lay your money down. There is a lot of great information here on DC.
Let me clarify this final statement, less someone say GearHead says it isn't possible, then I'll step down from my soap box. You can get a perfectly acceptable finish using OTC products there is no doubt about it. That said many of the commercial or detailer specific type products make it just so much easier.