You don't need to become a Class III dealer in order to buy Title II firearms (full auto etc). You need a Class III license to deal in these firearms. In order to purchase an M16 (or any legal Title II firearm) for personal use you need to fill out the appropriate paperwork, get fingerprinted, and buy the appropriate tax stamp. Once you are approved by BATF then you can buy.
This will allow the purchaser to legally buy a Title II firearm from another individual or a Class III dealer, provided all is in order regarding legalities and proper paperwork.