So if you really want to dive into fixing this, the first thing I would do is to measure the current going into the IC. Yes...easier said than done, but that will give you a big answer about heat. According to the data sheet, it should be 80 to 200mA w/no audio. 12V x 0.2A = 2.4W. That's how much power it dissipates just sitting there, worse case.
For now, let assume the power supply is not an issue since you tried two. And for now, let's also assume the circuitry driving the 3730 is OK, but could be the culprit too - but one thing at a time.
Also look at C3 (or whatever it is on your specific IC you're focusing on). That keeps the amp from oscillating, according to Fujitsu. It could be oscillating and you would never hear it, but it could be going full bore w/o you even realizing it. Ironically, it looks like DE used a 0.15uF, whereas Fujitsu shows what appears to be a 1uF. Check C2 and C4 too. Just guessing those provide a high(er) frequency termination. Just a WAG, but that might also lead to an instability too. Fujitsu recommended a mylar cap. C14, if leaky, could be causing a DC offset. I wouldn't discount that either.
Another simple thing, but very important - clean up the heatsink and apply new thermal grease. Not much, just a thin layer. That helps wick away heat from the IC into the heatsink. Is the heatsink soldered to the board (I don't have a clue if it should be). If it is, check those solder joints too because the heatsink will xfer the heat into the board (usually a bunch of ground plane). The amp could be fine, but if the heat has no place to go - then that is an issue.
Hope this helps. Not much to wrong w/the chip - not a lot of parts involved. Just looks like high power op-amps. But I tossed out a lot of comments, hopefully you can start to narrow it down.
here's a link to the 3730 data sheet: https://www.datasheetarchive.com/pdf/download.php?id=3bb4dd06dc8fa38fc4bd4c8a5c4e0e19205382&type=M&term=mb3730
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