I gotta say, it calms be a bit that even someone who know what they are doing messes up a board every now and then.
You don't want to know how many PCB "coasters" I've got around here...

So when you thought you fried it, what were the symptoms? Would it just not register on USB or take a sketch upload?
Intermittently wouldn't be recognized properly by the OS; wouldn't be recognized properly by the Arduino IDE (didn't show up in the "Ports" menu); when it did show up the upload process would fail; killing the Arduino IDE and relaunching it along with a reset of the board would end up with two entries in the system USB tree for the board... it was a mess. I had also thought it might be a Catalina issue; owing to the fact that I had just upgraded the OS on that machine (and there was an open issue for the Leonardo bootloader being nonfunctional on Catalina); but given that it seems to be working now I don't think that was the issue.

I ask because I have several boards that I think would work if I got a new bootloader on them, but I had tried that a while back with no success.
Depends on the exact board and symptoms. ARM based Arduinos and the Leonardo use a direct USB connection; all the others use some sort of USB-serial chip (FTDI, CH340, ATMega32u2, etc).

If it's a USB-serial chip based Arduino, the board won't show up at all when plugged in to a known-working USB port & cable, and you know that the PC side has working drivers on it; then the serial chip is dead. If it's a ATMega32u2, then that might have gotten corrupted (and is re-flashable, there's an ICSP header on the board specificaly for this); but if it's one of the others then it's more-or-less non-repairable.

If it's a direct-USB Arduino, or the symptom is anything other than not showing up at all; then software corruption on the board is a possibility; re-flashing the bootloader & a sketch with a programming tool might help.

Or... they might be toast.

Some of those boards still run the sketch that is on it, but wont connect to take a new upload.
Highly probable that it's either the USB-serial chip (if it has one) or the bootloader.

What board do you select when uploading a sketch on your clone?
I've been selecting the "Arduino/Genuino Zero (Native USB Port)". As far as I know, the practical difference between most of them is just the Arduino-pin to CPU-register (and thus physical pin) mapping. However, the listings for "Programming Port" are actually setup to connect to a programmer/debugger module (the Atmel-ICE is one, and the Atmel Embedded Debugger that's on the official Arduino Zero and M0-Pro boards is another).

Re: soldering station.
Well, I was in a bit of a chicken-and-egg situation, so I ended up just buying a T-12 compatible one from Circuit Specialists yea many years ago... it still works, so I haven't replaced it. Only thing I don't like about it is that it always comes up at 350c when it's turned on...