Maybe I am missing something here, but if the stated goal is a lower cost version, how is creating a pre-built custom breakout board going to cost much less to manufacture than the current Arduboy boards?
The Pro Micro has the benefit of massive volume and Chinese economic games that have reduced the price to barely more than the ATmega32U4 itself. A lot of the homemades already use this board. The biggest challenge is the non-standard pins. @Mr.Blinky’s homemade boards package makes this easy to get around, but with the inconvenience of having to re-compile everything. If the Pro Micro was used in an official kit version, hopefully we would get better/easier compatibility. If I remember correctly, the .arduboy package format even supports having multiple .hex files meant for different versions.
So, my vote (for a non-solder version) is the Pro Micro, with a 1.3" SH1106 OLED display, both of which are cheap and easy to breadboard. There could still be an un-populated PCB that could be used when ready to move off the breadboard. It would be nice if the PCB had support for the all the common OLED display sizes (1.3", 1.54", 2.42"), so the user could choose which they wanted (they don’t all need to be included). Also, the PCB should breakout all the pins so it is easy to hack-in other expansions. It probably should include a flash cart as well. Maybe design the standard kit around (3) AA or (3) AAA cells. The user can always modify to li-ion on their own if desired. It might be hard to design a case that would fit everyone’s needs, so maybe don’t include one by default. There can always be a library of 3D printable designs for various options.
I would still be interested in knowing how much cheaper you could produce a kit version of the existing Arduboy as well. Something that isn’t pre-soldered or pre-assembled.