I don't think there is any good or easy answer to the painful bra situation. I jokingly tell folks I have fi-bra-myalgia, but really, it isn't that much of a joke!
While you are searching for a solution you can live with, here are some of my suggestions. First, buy some "bra extenders". They are very cheap and you can easily buy them online. Get a 3-pack. Then try them on your existing bras, using as much extension as you can get away with (you can string them together). They might ease the pain just by making your bras too loose, but hopefully not so loose they don't work at all.
It might not necessarily be the underwire that you can't tolerate; I have one underwire bra that I can usually tolerate for a short spell for a worthy occasion, if I sit up very straight (any slouching makes it very painful though.)
Whenever you are home/alone, let those puppies hang free. Find a top you can wear that covers most of the disaster area, just in case someone drops by. Try a few different types of camisoles that have a built-in bra. Do not expect the same level of support you get in an underwire, it simply won't/can't happen, but it should bring things up to the level of socially acceptable. I usually have to sew the straps up a few inches at the shoulders to get them to fit right.
They do have bra-free bras, invented for occasions such as wearing a strapless gown. I have looked but not tried them because I don't think the stickiness would get along with my sclero-skin.
You can also think outside the box, such as using the top part of a two-piece swimsuit if it fits you nicely. But my best suggestion is to just let those puppy ears droop as low as they need when nobody else is around, because every other solution adds a bit of pain and you probably don't want to exhaust yourself trying to cope with the pain 24/7.