I have a 16" 300 BO and was thinking about going to a 8 to 10" barrel. When I apply for the stamp can I use the serial number on the lower that the 16" barrel is on?
Yep. You're basically adopting the markings of the existing firearm. Serial number and model. It also needs caliber, which is often on the barrel.
You'll just add the registered owner's (trust/corp/you/etc) name and the city & state where you actually make it (doesn't have to match the mailing address on the Form 1).
Here's a document that's pretty clear on it, especially considering the ATF published it: ATF Ruling 2013-3. (It's not new rules, just a pretty clear ruling explaining the steps using existing regulations). Note: they do add "pistol slide" as an acceptable engraving location.