I don’t have enough experience to say somthing about the PCH being resoldered. I with my simpy unexperienced mind would maybe think that this region did get some heat looking an the 7 solderblobs under the PCH and be a little concerned for the solder under the PCH itself. But as written, no experience.
Yes, the only way I can think of ti fix this possibly is to use a programmer.
Regarding the rest- you downloaded the Intel tools already and you have a proper dump (=backup). So for the cleaning it’s just following the guide to the letter. The other part won’t be too difficult either.
But there’s no warranty, given the history of your board and what it’s been through I’m not too optimistic.