The schematic for this looks like ampretty much run of the mill class AB amp channel . . . no magic there, and pretty easy to work on. Looking at the pics, either I'm not seeing something on this tablet, but the board does notlook too bas to me either - I can really only see one fubar heavy trace, and suitably heavy wire on the surface of the trace will work fine - just keep it snug and where the missing part was, and EMI and such should not change enough to care.
I assume the power supply has been tested to be OK (and it's certainly beefy to have eaten this much and survived.
I will speculate on failure based on what I have encountered, but remember, it's not on my bench, so I'm jusf applying my experience with similar ampsmto what you have offered . . . .
In the "end game", what you have is that both sets of output transistors (3 to the positive rail and 3 to the negatice) have failed to a short circuit such that it ate emitter resistors (the .47 ohm devices), and ultimately blew a foil apart instead of a fuse, thus stopping current flow. The issue of why is harder, but there are a couple typical scenarios:
1) An single output device on one side failed to a short. (This would basically cause the output to be pure DC at that point) When the opposing side tried to conduct, it would basically short the supplu, producing a lot of heat on those devices, and failure in short order, resulting in what you see.
2) Kind of a variant of the above, and which seems to track better with the description of the failure. Due to a weak/defextive device, driving too low of an impedence load, or phase of the moon, an output device on one side (maybe more) failed to open. The amp would still work, but the surviving output devices on that side would be working far harder than they were intended too, and likely would have run very hot making at least that section of the heatsink seem much warmer than normal. Continued use this way caused one of those devices to fail to a short, dropping right into scenario #1 above.
What really can't be absolutely determined is why . . . but typical are bad load or obstructed cooling (I serviced amps for a couple of clubs, and it was interesting that the failures were always so similar that I could get most of the parts ordered before I saw it, and the observed cause was alway massive bar-funk buildup choking cooling air off. This looks really clean, so I tend to speculate this is a "driving too low of an impedance" type of failure (even if the cabs are labelled fine, a failing driver can drop in impedance as well . . . gotta check everything.
One other thing to consider (and you have been "there" to check it's condition) is that heatbsink compound frequently degrades with age (or the assembly tech skimped) and that could have caused an output device to overheat, triggering this failure.
While I typically don't find all output devices failed (typically, on the side that went first, since the current dump is through the failure, others survive without being stressed) but it sounds like you did, I'd replace all failed outputs, and have a good hard look at the driver transistors (TIP41 on one side - I don't recall if both sides are the same) since I often see these faults take those. Typically, most prior to that survives . . . . Check the emitter resistors closely, since they take a beating in thisntype of fault, and any thing else that looks baked - find it on the schematic, and see what it does (I can't tell what part the burned larger resistor is on your pic, but it would be typical for that to be the emitter resistor for the first device to short). With the power devices out, you should be able to meter/test the remajning resistkrs and diodes without issue.
Be sure to check every fuse in this thing and ensure that is the correct type and rating! I am somewhat amazed that a PCB trace failed before a fuse (and no, I have not taken time to review fusing on the schemo. . . )
With finals/drivers out, bring it up current limited and see if you have proper signal at the inputs to the drivers. If you do, start repopolating. If not, you need to work back upstream until you do. Once repopulated, again come up current limited and do a basic test, and leave it on for an hour of so. From here, it's kind of up to you, but I tended to run the bar amps into a minimum rated impedance dummy load using typical program material at just the edge of clip for at least 8 hours to stress test. (Actually used to use the first Madonna CD for this . . . ). If nothing else failed, it would go back, and I never had a repeat failure!
(Also clean along the way . . . I left that out here, but the bar amps started out with pulling the boards and a very deep wet clean with a soft brush and dry before starting, otherwise, everything go contaminated, and you wanted to gag being near it . . . Ultimately, cleanliness should be the same as if new on a repair as I see it . . .
And lastly, myself, I'd trust a proper repair far more than new. First, all other components have been run and tested over time (so no infant mortality in the front end). And I trust my work. (And frankly the misguided level of paranoia about using repaired gear here I find quite amusing. If I had a buck for every fictitious statement I have heard on the topic, I could retire! (That, or that are an awful lot of hacks in the biz making others experience differ)
(And my apologies if I am rambling, bad grammar, typos, etc. . . . I had a pretty major surgery last Friday, and while I'm off the "Good stuff" the muscle relaxants and such are still messing with me)