After talking with Space Guy, it appears that his code somehow prevents the %client.hasSpawnedOnce variable (Used by my code for toggling wrench modes) from being set to "1".
The fix he recommends is this:
1. Open "Add-Ons/GameMode_TeamDM_Base.cs"
2. Search for the line "%this.tdmspawned = 1;".
3. Change the line to "%this.tdmspawned = 1;%this.hasSpawnedOnce = 1;".
4. Profit.
This should permanently correct the issue.