Update: Finally got the plug and put everything back together. It runs great! I only ran it for about 5 seconds though.
Except I switched the heads. Before I assembled the heads I noticed that the only apparent difference was the hole on one was threaded. I now know that those threads are for the brass pipe to the EGR valve. Whoops! Looks like I'll be doing it all over again... tough lesson to learn.
I hope this is the source of the massive oil leak coming from the R side (where the threaded hole is now facing forwards).
I have smoke coming from somewhere on the L side, I can't figure out where. Either somewhere around the transmission or through the valve cover. Either way it's very concerning and I'm not running it again until I figure out what's going on. There is trans fluid around that side from a hose I forgot to tighten.
So, overall, a bit embarrassing and a bit more work but maybe someone will read this and avoid the same mistake!