I realize what I've mentioned below was presumably covered by Avalara but perhaps not in the way I'm describing. Also I say with complete objectivity and certainty that neither Avalara nor TC know much about their apps in terms of how they integrate with Sage 100 under the hood. Maybe their engineers do but not Support. I need to meet Ed Feliq apparently.
Sorry for the length but I hope this helps. I think it will at least get you further.
Since you are running Sage 100 Adv or Prem, the **CORRECT WAY** for them to answer the question about whether AvaTax is working fine is to remote into the machine where the actual TC program runs and start up Standard / Mas 90 style. Don't start up the normal way. Then simply go into S/O Entry. If you get an error, boom it means AvaTax DLL is not registered and the TC program will never be able to create the SO. That's how they should have tested with you.
I looked at your Word doc showing the screen blips. It shows AvaTax is not registered on the TC machine. Try it like this:
1- Remote into the actual wkstn or server that will run the TC app. There absolutely is a machine where their program is running even if they say otherwise. It might be the server that's running IIS. Regardless, it runs as a BOI app, which means Mas90 style.
2- Create a folder on the that TC machine in the local C: drive called C:\Sage
3- Copy the \mas90\Avatax folder from the Sage server so you have a C:\Sage\Avatax
4- Edit their BAT file and add a line with the word PAUSE then save the file and exit.
5a- In File Explorer, rt-click and Run as Administrator. The PAUSE will pause the BAT file but you get to see if any portion of the DLL / TLB registration failed. If it didn't then woohoo. Press the ""anykey"" to close the command prompt window then start up Sage via Mas90 style and go into S/O Entry again. Once that's good, try TC.
5b- If 5a had an error then try this way to register:
* Click Windows key then press X and choose the Administrator command prompt. If you don't see it, type cmd.exe then in the search result rt-click on cmd.exe and choose Run as Administrator.
* Then type: CD C:\Sage\Avatax
* Once in the folder type: START /B register_for_com.bat
(Verify that is correct name of BAT file).
* Rinse and repeat rest of 5a