CWC,
You'll need sealant #88861417, Dex VI quart # 88861037, SEAL #89059495, GASKET #15642511. You may indeed have the newer TC, VINs above that number had T-case manufactured with fill plug holes raised for the require fluid level, also if you don't have a sticker on the TC or owners manual notation your probably okay regarding that issue.
Your right Hummer service was absorbed by different GM dealerships, if you can find one they "may" have a trained mechanic certified for Hummers, he would have been alerted to the TC issue as well as a host of other problems specific to the line, don't expect the average GM mechanic to have a clue.
Imagine the number of vehicles traded in because original owners and local mechanics were puzzled by all the problems with the H3 and a corporation known for trying to wash their hands of faulty engineering, years later now 2nd and 3rd owners are caught in the shuffle of misinformation and vehicles never serviced properly. Hummer Forum is very helpful.

 

I'm a bit confused about seal #89059495. Looks like a GM output seal, but showing not compatible with Hummer H3? The part number I saw for the H3 output shaft seal was #88935685. I'm not seeing your number listed on the component list for the H3 case...was that a typo or am I missing something? Does this really need to be replaced?