The following are very simple questions, they are not meant to be patronizing. The goal is to find out why your version is incorrect, despite your inclination that it is correct.

1) Why do you know you are running version 1.10 of Diablo2 Lord of Destruction? What version did you start with, and how did you change it to version 1.10?

I purchased and downloaded the game yesterday so it automatically updated itself to 1.12 (or maybe 1.13). I downloaded the RAR file on the Unleashed website to convert files from 1.11+ to 1.10.

2) What version of HU did you download? Provide a link that proves you used the most recent version expected by the Arimyth Gateway.

http://eu.mirror.files.arimyth.com/Hell_Unleashed13a_Full.zip

This is the link I downloaded and installed.

3) After you installed v1.10 of D2, and after you decompressed the HU files into the installation directory of v1.10 of D2, did you run the d2modsetup.bat file? Perhaps run it again, the message "Do you want to install [or uninstall] the mod?" is a bit of a misnomer, since I understand that this file is just part of a modding package, not something Soulmancer himself created. In fact I one heard that the message of install/uninstall doesn't actually do anything, it's just some flag in a .dll file that gets toggled but doesn't get referenced.

I did run the d2modsetup.bat file. It updated my d2 to the Hell Unleashed Mod (title screen says it, with credits to Terry (Soulmancer). I also had to download a NewLoader.exe because the HU one for some reason was not recognizing my game as a digital copy and kept asking me to insert the CD. Maybe I messed up an installation step or is that typical? I feel like i found the instructions to use a NewLoader separately from the standard instructions

4) How do you know you are connecting to the Arimyth Gateway?

It says Gateway: Arimyth on my Battle.net realm list. Not sure about the actual details therein since I cannot see them

If you do not want to troubleshoot each of the steps above, then just consider a reinstallation from the beginning, as that can be faster. These are the basic steps:
1) Install D2
2) Install LoD
3) Patch D2:LoD to version 1.10
4) Overwrite the files in the D2 folder with the HU files
5) Run d2modsetup.bat
6) Start D2 using the "Hell Unleashed.bat" file
7) From the title screen verify that the Arimyth Network Gateway is selected below the Battle.Net button and then press the Battl.Net button
8) From the character selection screen, verify that the Current Realm in the top-right of the screen is "HU". You should now be able to make a character.

Yea, I sometimes know that it is just easier to reinstall. I may do that, if I cannot re-mod and successfully login. Should I just Uninstall Diablo II using the generic Windows Uninstall, or is there an uninstall file associated with the game? (am not home at the moment, cannot check). I did make a copy of the original game (LoD, I think) to a separate folder before I modded to HU - is it easier to just copy/paste it over the current folder/files, or would a full reinstall be better? Either is fast

Problem is pvpgn doesn't recognize if you have patch 1.10 or 1.13, you still can log on but fail to join games. So problem isn't with game installed. It's a firewall preventing you to join server. But well, I may be wrong.