I think the solder melting thing is related to the resistor. The blower motor, from my experience, seems to be a bearing issue. Unfortunately, they aren't serviceable but the good news is they are easy to replace.
You can get a replacement after-market blower motor for ~$55 on Amazon or cheaper if you can find one at a junkyard (which is what I did).
Yeah you're correct, fan only working on 4 is the resistor (which I understand isn't your problem). I'd check the blower motor next. It's only 3 screws. Pull it out and see if it spins freely. If you give it a spin and it feels like the bearings are lubricated with peanut butter, then I'd replace it. That's what happened to mine. This could cause a resistor to fail prematurely so I'd check that again, too.
The bummer is you cannot service the blower motor. Replacements are in the ballpark of $450 for genuine Honda part and ~$55 for aftermarket (Amazon). I got mine at a junkyard. The only Fit in the yard was stripped pretty good but I lucked out and it had a good working blower motor and resistor. Only cost me $30 for both.
BTW, since the space is pretty cramped, this screwdriver makes pulling these parts a little easier.
Hope this helps!
Had the same problem this spring. Did some digging and there are tons of other Fit owners with the same problem that almost universally cited the blower motor and/or blower motor resistor. Dealership quoted me $450 for the repair ($250 parts, $200 labor). Ended up replacing both myself for about $65. The whole process took about 15 minutes.
It is not a remotely complicated repair, but both parts are located in an awkward place if you aren't a tiny person. They're both accessed by removing the tiny panel under the glove box or the box itself. Only ONE tool is required, which is a Philips head screwdriver, but I'd recommend using one with a very short handle to get at the resistor's screws (mine was about 2.5-3" long).
Was very glad to get my AC back in time for summer without dumping an unnecessary $390!