Just wanted to pop back in here and confirm that everything worked perfectly.
I downloaded the .TXT file for MAME 0.139 from the link, renamed it to .DIFF, downloaded the Headsoft MAME Compiler program, applied the DIFF Update, compiled my own version of MAME, ran it with -cc to configure the MAME.INI file, and finally edited the MAME.INI file to add the three lines required to remove the nag screens.
Yes, it's a run-on sentence, but it makes the point. It was easy, and I thank you for the help!