MS SQL Server: Transactional replication not working but no errors are present
I'm still not sure what the issue was because nothing indicated a problem, but the fix ended up being to just generate DROP and CREATE scripts on the Transactional Replication Publication using SQL Server Management Studio and running them. After which, I had to reinitialize and generate a new snapshot since it was a new Publication technically.
I guess the old turn off / turn back on again trick for the win.