You're jumping the gun a little bit.

The adjust failure normally has to do with a dead, missing, or otherwise undetectable battery.

You can bypass this message using the coin door diagnostic buttons (either escape or enter--I can't recall off-hand). I would recommend *not* replacing the battery holder--just remove it. Then, either use NVRAM or a remote battery holder.

http://www.pinwiki.com/wiki/index.php?title=MPU_Battery_Replacement_Options
http://www.pinwiki.com/wiki/index.php?title=MPU_Battery_Replacement_Options#System_11.2F11A.2F11B.2F11C

The only time you need a fiberglass eraser or need to do bead blasting is if there is battery damage from a leaking battery that needs to be addressed. Does your board have battery damage?

As for the jumpers, they were likely installed for a reason--usually because of a broken trace. Find out why they are necessary first, before thinking about removing them. Getting rid of them without understanding why they were added in the first place could cause new problems.

The changes look a little messy but look like they would work. I would leave them be. Clearly they were done for a reason. The third picture, is something you commonly can do when the pads flake off (or if you're awful with a soldering iron and burn them off, looks like that guy did) to successfully complete your work, he was just soldering on that transistor further on down the line since the pads it is supposed to go in were burned off.

The jumpers are a little messy but in the end look fine. For the second one, must be that traces were damaged top-side, but again, I'm just noting that and you should leave it be.

If it boots now, definitely just leave it be!