I have a pretty big issue with my 1986 Pontiac Firebird. After the car has been running for a few minutes, white smoke starts coming off the engine and leaks into the cabin of the car. The smoke from the engine appears to be coming from somewhere on the back left of the bay(passenger side), but I can’t pinpoint exactly where. It’s progressively gotten worse over the last few months. It’s not an oil or coolant leak, as both have been checked and any broken parts have been replaced. The smoke also comes into the cabin through the A/C vents if they are turned on, and it comes up through the space around the E-Brake and center console area. Transmission was also replaced awhile back so I don’t think it could be an issue with that. The white smoke gets so bad in the cabin that it makes it hard to breathe and causes headaches. Doesn’t smell like coolant or oil, DEFINITELY smells bad though. Has anyone had an issue like this? And ideas as to what the heck could be going on?
(Forgot to mention the engine is a 305 V8 with about 300,000 miles on it. Head gaskets have recently been replaced)

 

Smoke = something burning (duh... I know you knew that... just need to get it back out in front)

Avoid the tendency to overthink it. Something is burning. Find out what it is. Obviously it's happening at a place that something is hot. Hottest thing under the hood is the exhaust. Whatever is burning is probably doing so on an exhaust part.

Either it's a fluid of some sort, of which there are only a few available; or it's something plastic. Fluids include oil coolant, trans fluid, brake fluid, PS fluid. Plastic wouldn't last very long. Although it could be something creepy like a shopping bag on the Y-pipe. But I'm sure you've already examined the exhaust closely, right?

Given that juicy tidbit of info, my money would be on coolant: whoever put the motor back together either didn't use sealer on the head bolt threads, or they used RTV.

 

Here's an answer that will help.
Most greases and oils will burn white and stink like hell when they hit the exhaust, engine, PS fluid, and especially transmission fluid will stink and it doesn't take much; your doing some investigative work. Check the valve covers, Check the distributor seal and oil pressure sending unit, on the back of the engine Oil pan, dipstick, and rear main seals they will crack and leak. Not very likely but also heck your master cylinder and brake lines in that area for leaks.
If you switched to synthetic oil you discovered a leak that already existed because the the chemistry of synthetic oil has washed the debris out especially valve covers and mains. the only repair is replace the gaskets. You had the transmission repaired its possible they over filled its possible you have a cracked line or fitting, or the transmission was overfilled blowing fluid out the breather tube, and getting oil onto something hot.