with no file info it is all guesswork
My current question is: Why, immediately after a normal full system scan, would a bootscan of the same files turn up more threats
Again we don't know the files are or what the threats are.
The boot-time scan is different to the full system scan and these differences that could be the reason.
The boot-time scan, includes archives and it also scans for PUPs = Potentially Unwanted Program/s - See
http://searchsecurity.techtarget.com/sDefinition/0,,sid14_gci1066761,00.html. Not included in this definition are tools which can be used for good or evil, some have been legitimately installed for a specifically good purpose, but could have been unknowing installed for a malicious purpose.
Hopefully you can see why we need some information on what was found, file name, location and threat/malware name.