Just use same SoC as RPi 4 (whatever that will be) for new Pyra SoC board ...
Which will probably be at best on par with the current Pyra CPU.
While it's hardly the best metric, Pyra Cortex-A15 is 3.5-4 DMIPS/MHz. Pi 3's Cortex-A53 is 2.3 DMIPS/MHz - about half the efficiency. That's the compromise you have to make for such a low price point. It is, however, 64-bit capable compared to the A15, which is only 32-bit capable, but right now this is a moot point due to the Pyra topping out at 4 GB of RAM. Any CPU with over 4 GB of RAM though would definitely need a 64-bit CPU of some kind, and obviously some apps could probably benefit from a 64-bit version, so logically speaking, it makes relatively little sense not to have an upgrade CPU be a 64-bit capable one.
If ED wants to keep to ARM processors, I'd think the ones he should be looking at would be Cortex-A72, Cortex-A73, or Cortex-A75. These all provide a notable increase in efficiency over the current Cortex-A15 (all being at least 5 DMIPS/MHz, with the A73 being about 6.35). The main questions would be how much he feels he'd benefit from stuff like per-core cache (A72 has the least), how much he feels he'd benefit from two-way vs. three-way pipelines (A73 has only two way, the other two have three), if he thinks he will go over four cores (only the A75 has support for 1-8, the others are strictly 1-4), and so on. Even then, all of this has to be balanced against stuff like heat produced, power consumed, and if it'd be a truly tangible boost to performance of the device - if it ups heat and battery consumption a lot but only gives about 20% more performance, is it worth it?
And even then, he's got to find someone who will sell them to him in bulk quantities. Qualcomm turned him down, nVidia isn't interested without full manufacturing control, and so on. It's not like desktops where you can just go to an online store and buy the processor you want.
Intel Atom would be the next-most possible chip, but of course, then we'd be taking a big leap up to x86-64. Debian does run on x64, so that won't be a problem, but it automatically doubles-up the amount of testing and maintenance that needs to be done, as well as that apps that would be compiled as DBPs would also need to specify what version they are (DBP = ARM, DBX = Intel), or be some kind of "universal" app (DBU) that would work on both. The other kicker is that at best, it'd turn the Pyra into a GPD Pocket clone. (Although some might not feel that's a bad thing.)
And no matter what, it's got to have a GPU - preferably with open-source drivers, because otherwise, we have to either hack and kludge around the GPU, or not have a device that's as open-source as he'd like it to be (which also prevents it from having more support than whatever its manufacturer decides to give it). Something like this could literally extend the life of the thing by years.
So in short, figuring out what the upgrade board should be isn't a cut-and-dry process. It's got to be something he can get in large quantities, if it's not ARM v7-A he has to support a whole other instruction set, there are binary concerns if he picks an architecture that's vastly different, what GPU it has and what can be done with it, and so on. It's not an easy choice to make.
