13 judges is a compromise position. Even better: all 179 circuit judges plus 9 current SCOTUS members with lifetime tenure. Pick & recuse 13 *random* judges from nationwide pool for each appeals court case. Those *random* 13 judges = SCOTUS *for that case* if it goes that far. No amendment needed.
I think the "thirteen districts, thirteen justices" thing is a good talking point to counter, particularly if Dems promise to only nominate justices from districts with no representation. blah blah blah good hardworking Americans in flyover country deserve blah blah blah, etc.