My apologies for not being too clear. The anxiety from thinking I just lunched my engine was a bit overwhelming. Haha.
Ok, for the first part, "barely wanted to run," it was an extremely rough idle. Almost like bad fuel and could barely take any throttle. My 312 has the "one touch" starting thingy, so it would only allow the starter to engage for about 5 seconds. I tried that about 4 times and on the 4th, it started, but with a rough idle. It ran for maybe 15 seconds and then died. Did this twice and it finally smoothed out a bit and would stay running.
As for the source of the smoke, I still have no idea. No leaks anywhere, no oil spots, nothing. I installed a K&N 204 filter (the correct one for the bike) and there are no leaks from that, either. The smoke from the engine was coming up between the air intake tubes in the cockpit. Almost like there was oil on the header, but there was none. The smoke coming from the exhaust was light grayish-blue and smelled like fuel and oil.
I just got back from a short ride (started out very worried, but I got better) and it runs just fine. No smoke, no roughness, sounded and ran perfectly fine. I'm guessing there was just too much oil in the bike. I put 3.7 liters in when I did the change. Did it with the bike on front and rear stand. Hopefully no issues in the future! I appreciate you looking out for me, though. I felt like a bit of a knob posting this, but maybe it can help someone if they run into the same problem.
And just to keep some dignity, this isn't my first oil change on a bike. Did my old F4, my ZX14, my ZX10R, my Husky 610SM, my Yamaha BT1100, my Aprilia RSV1000R, and my Yamaha XT660Z Ténéré with no issues at all.