Dealing with a chewed-up multilayer PC board

I'm working on a friend's subwoofer amp and I'm worried about one of the eight-pin DIP IC locations. I'll skip over the history to get to the important part. This one IC location has gotten badly chewed up - there's a chance someone was in there before me and worked on the same IC. By this point some of the pads on the non-component side are missing; I'm not so worried about missing pads where there is no trace on that side but there are some pads missing where there are traces leading away. There is at least one layer of traces buried within the board. I intend to put an IC socket there like I have for all the other ICs but I'm afraid that if I go ahead and solder a socket into place, I will be left with some open connections and I'd never be able to troubleshoot it especially since I have no schematic and apparently the universe has made it unobtainable.

So I have an idea to proceed forward with and I'd like to know if any of you have a better one.

It turns out that I have some 3/64" brass tubing that was obtained from a hobby shop. I thought what I might do is drill the PC board holes out with a 3/64" bit, scrape away the green coating from the traces I can see on both sides, tin the outside of a length of the tubing, cut the tubing into roughly 1/8" lengths, insert those lengths into the holes I drilled out, and heat them up with an iron, also soldering the tubing to the traces where they exist. I've already verified that the IC socket pins will fit within the I.D. of the tubing without difficulty. It may be a bit tricky to solder the IC socket to the pieces of tubing; perhaps the socket's pins have to be held partway out of the tubing for that to work. My hope is that when heated, the tinning on the outside of the tubing will grab any embedded traces.

Does anyone have any thoughts on how I should involve flux? I have both liquid rosin and paste flux.