LOL my bike is working great, and I can't understand it!

Seriously though, when you shifted into the big cog, and then 'shifted down even though it was on the biggest cog already a couple of times', you felt the shifter giving tactile feedback of shifting mechanism happening? Like 'click' and everything?

Are you sure you don't have your cable(s) way too tight and wanting to send stuff off the cassette (but limited by the limit screw)?

That doesn't really seem to make sense, but I can't make much sense of your reported behavior either, just spitballing.

All the cables and housing are well-seated in their ferrules and stops?

When you were trying/failing to shift up, did you get the typical shift/click sound/feeling but nothing happened at the derailleur? Or was the upshift lever frozen? Or did it move with no resistance?

Are the derailleur(s) pivot mechanisms lubed and freely-moving? If they are not, that would explain how the cable could pull them in the big direction, but the derailleur-spring not being able to force the derailleur back to small direction when cable is loosened, and maybe working it through the first time cracked them open?

Where near the LA river do you live, and when do you ride, so I can stand down there and wait for a free bike?

Meanwhile I agree with 10 Wheels, if it's working, keep riding, just gradually expand your range from home as your confidence grows.