OK, what is blocking the PCB holes?

Probably just holes with more copper contact than the others making the heat from your iron dissipate around the hole instead of in the hole, ground pins are usually denoted by different shape... square

if you don't want to risk more heat then I would suggest getting some micro bits and hand reaming the holes as the solder is usually soft enough to do it in less than a minute per hole.

just be careful to stay in the center of the hole and start with a smaller bit than the hole or you risk drilling out the via, those holes are probably linked to the VCC grid... don't have a schematic in front of me or I would know

EDIT: just remembered a technique I use every so often... when trying to desolder small parts that are hard to get at try mixing some lower melt solder in there first as it will make the existing stuff a lot easier to remove.

Well, I didn't have any of the chipquick stuff, but I did add a blob of my regular solder, and maybe it was lower melting point, or maybe it just retained more heat, in any case I finally got the last hole sucked clean. Thanks everyone for all the good tips!

I was planning to try and figure out where to add wires for additional power to run a QU-BD heater, but I figured I'd add the missing headers while I had the board out. That took so much time that I guess I'll come back to the power connections some other day.

Anyway, I got it hooked back up, and printed something, so I didn't destroy anything. I even tried testing the PWM fan with the manual controls in RH, and it worked properly, so at least one of the added headers is also working fine.

I second the use of Solder wick... saved my butt on many occasions (long ago gave up on a solder sucker.)  I've done a ton of TH and SMT solder work, and I really like Mouser Part #: 577-1808-10F. But as with anything, you'll probably get a bunch of recommendations

-Mike