Maybe the code has to be modified to first load R0-R7 directly and save them on the stack, then move (
mov) a higher register into a lower register
Yes, that sounds reasonable. Spill a low register to the stack and use it as a scratch register.
So while the Cortex-M0+ has these registers, somehow they can’t be used in a store word instruction, which seems weird to me.
Looks like it’s due to the dense encoding in the Thumb-2 Instruction Set! There is just no more free bits to encode more registers 
Some more details here
I am deferring my work on the TeensyLC (there are a few more reasons) and hope to find the time to pick this issue up later this year. I think the information here is quite helpful already, but there is no real solution right now (assuming we ignore “It’s not possible” as a solution). Hope it’s fine to leave the ticket open for so long?