Now I'm designing a PCB, and what's lacking is good part placing and trace routing. I feel like there should be a an algorithmic way to do what I'm doing by hand. It sort of reminds me of the traveling salesman problem.
They exist, but NONE of the PCB designers I have worked with, all of who have worked at multiple big name tech companies and still do, use these tools.
Do the work. Even something as simple at a guitar amplifier needs attention to detail, to route ground currents away from where they can cause noise. Even something as simple as a guitar amplifier needs attention to the current handling needs of individual traces. Even something as simple as a guitar amplifier needs attention to the detail of proper component placement to minimize inductance where necessary between bypass caps and their associated IC's. DO THE WORK!
That's one nice about (tube) guitar amplifiers: max current is at the power supply pin, about 72ma, despite transferring 27w or so. So your voltages are pretty high , but your traces can be pretty thin. The big thing is leaving plenty of space to prevent arcs.