Made some advances, and i think i am almost ready to lay down the traces (changes will be more difficult after that).
I implemented the in-rush current limiter circuit discussed above. It will be optional: will leave the footprints at the bottom side that i will populate only if necessary. In the case i need to use it, i just need to solder the necessary parts and use the new connector (below the 5 others) for the power input.
I have also decided that the amp PCBs will be printed with 2oz copper but the control board will be 1oz only, to reduce cost. This PCB will be the one carrying more current, but only in one single trace that is very accessible and with no components on top, so i decided to leave the power bus trace without solder mask and tin it manually. Will be the first time i do this, i hope it works. I don't know if there is a problem with this approach
Another thing i have been dealing with is how to connect the heat pipe to ground:
TI explains that the heat sink (in my case heat pipe) must have a good connection to the PCB ground, the reason being it is a noisy device and could increase the noise in the amp. It is not enough to leave the connection to ground depending on the contact of the heat sink with the pad on the chip (that is also connected to ground). Their recommendation is to use heat paste between chip and heat sink + screws between heat sink and PCB ground.
Obviously, i cannot do that with a heat pipe.
At first i thought that i could use liquid metal instead of heat paste between chip and heat sink to grant a good electrical contact (I would have to coat the the copper pipe, but that should be no problem). But i could not find any information about the material/compatibility of the pad on the chip nor its exact shape, so i abandoned the idea.
But this morning i thought about using a couple of spring load contacts. The ones indicated with arrows in the picture below have a height of 1.5mm when free and are aimed to work at 1.2 mm when pressed, that is the exact height of the chip. Let's see how they work.
Another detail i need to deal with the is, potentially, impedance matching of the oscillator pins. I will be connecting the clock of the master board to the other boards through cables. I will have to find out what will be the best way to avoid potential issues beforehand. The frequency is not very high, but the distance between chips yes. TI does not make any provision about this in their evaluation board, maybe it is a non issue. I am not sure if the 3E audio boards (that expose the connectors to set their boards in master/slave mode) have some sort impedance matching. Will have to see what i can find out online....