95 F150 302, 5.0 Distributor Install Frustration

My F150 recently died while driving and wouldn't restart. Upon towing it home, it restarted fine, so it was having an intermittent electrical problem. It displayed a CEL code of 211, which is a PIP circuit fault. Upon researching I found that it was likely either something in the distributor was bad or that a wire near the PIP was grounding.

I purchased a re-manufactured distributor and installed along with new plugs and wires (the firing order is 1-8-4-5-6-2-7-3). I made one mistake during the installation and fired the engine with #5 spark plug removed...likely pulled air into the open cylinder. Now the engine will fire, however it is a very rough idle and will cut off after around a minute. Also, I noticed oil blowing/dripping from the rear exhaust. It no longer displays a CEL code, and I re-installed the old distributor to confirm the re-manufactured distributor was ok. It reacted the same way, so I've since reinstalled the new distributor.

So, would firing the engine missing a spark plug throw off timing? I'm about to clean the O2 sensor since it likely is coated with gasoline/oil in my exhaust system. I haven't done the process where I find TDC and check timing...was hoping to get some insight before I potentially made things up worse.

Thanks!

To clarify 1-8-4-5-6-2-7-3 is not the firing order...that's the order on the distributor cap beginning with 1 and firing clockwise. The actual firing order is 1-3-7-2-6-5-4-8. Firing diagram attached.