Some good news in brief....
1) I flooded the bottom of the gas tank cap with WD-40, and the 2nd wing sprung out. So it clicks into the tank now.
2) I gave the tank a thorough cleaning (garden hose water flush, hot water rinse, shake with ice cubes, vinegar+salt soak for a few days, neutralize with baking soda, flush with water again, rinse with distilled water, rinse with isopropyl alcohol, heat gun, swish around some gas with oil added to it). It rides like a charm now.
The details:
After I drained most of the gas out of thank, I saw a lot of crud in the remaining fuel at the bottom. I also saw that the tank sealer I had put in a couple of years a go had delaminated from the tank walls in several areas. (This probably happened because I did a poor job sealing it: I forgot to mix the sealer and dumped it all in. Some parts were extremely runny, just liquid, others super goopy. It was so bad I decided to get another can of sealer and pour that in... this one I did mix, but now I was trying to get it to bind to the uneven substrate of the first sealer.) I would speculate that the chunks of sealer that came off the tank were starting to disintegrate and contaminate the fuel or perhaps the large pieces were physically constraining flow out of the reserve port.
I tried to scrape and get as much of the delaminated pieces that I could out, but I couldn't get everything. So.... this could happen again. I'm thinking next year I should drain the tank again and use long pliers to try to remove more of the pieces of delaminated sealer, use a vacuum cleaner to get out more. Any further thoughts on the issue (i.e. feedback on my tank cleaning technique, how to avoid flash rust [I waited at least 12 hours after drying to add swish the gas/oil and I believe I got flash rust... definitely around the tank opening] recommendations on if to reseal and how to prep if I do, getting more of the pieces out, etc.) are very welcome.
Thanks to everyone that responded!