From: Federal Way, WA
Just some things I ran across while looking for something else, which turned out to have nothing relating to your question. Maybe some of the links in some of the articles will help you find more.
This chapter and the next talk about the invasion and capture of Tinian:
Campaign in the Marianas, Chapter 13
Mostly photos, but 504th Bomb Group:
US Army Air Corps 504th Bomb Group, Tinian
A tiny mention within an article about one unit:
1st Battalion, 68th Armor Regiment, "Silver Lions"
Not directly what you're asking for, but an interesting article on Darrel S. Cole, a Marine bugler who spent a lot of time manning a machine gun at Saipan, Tinian, and Iwo Jima (where he was killed). I think we all know about the ship named for him, which was attacked off Yemen a few years back.
Wikipedia: Darrel S. Cole
Some on Sgt. Cole's unit (which didn't stick around after the island was captured):
1st Battalion, 23 Marines