The SAM9x60D6k has 64Mbit (aka: 8MBytes) of RAM on-board and available at $10 or so. Yes, its an ancient ARM9 (aka: ARMv5) but that might be an advantage in this case, since Palm OS5 is like ARMv4 or something. Its also fully documented, fully open source (Mainline Linux Kernel, open-source U-Boot, open source bootloaders, etc. etc.) so you'll have all the documentation needed to make a computer from scratch. (Unlike Rasp. Pi, which has some "Broadcom magic" drivers sitting around, the SAM9x60 is fully open)

I bet that 600 MHz and 8MBytes is far beyond what the Palm OS5 had as well, instead of struggling to get everything working inside of 264kBytes. SAM9x60D6k is on the order of 100mW to 300mW of power consumption, so definitely small enough for a passively cooled handheld.

Since SAM9x60D6k is an advanced-package that includes DRAM (soldered onto the package), the BGA-pinout is unusually easy. The documents suggest that a standard 4-layer PCB should be able to do the job (though OSHPark offers 6-layer PCBs at a bit more $$ if you aren't sure if 4-layer will work).

Trying to do this on a RP2040 is... ugggh. So many issues. I mean, I see that the point of this project is to have a challenge so I recognize that. But there's just so many obvious issues with the RP2040 that I can't help but think that other designs would have been far, far easier instead.