You know what would be a "fun" excercise?
The console output is always 7-bit right..
So if someone designed a tiny PCB with a CPLD or an ATtiny ARM processor or whatever on it and a few megabytes of flash memory.
Program the CPLD / ARM with some hare-brained protocol that only listens for and sends characters with bit #8 set high, and uses the remaining 7 bits for a minimal protocol that can exchange a couple opcodes like "read block" and "write block" over a 115200 8n1 serial console.
Connect it to GND+VCC+RX+TX on these tiny routers.
And write a small kernel module to reach the superfluous flash through this protocol over the serial connection.
Could even put an extra serial header on top of the tiny PCB where it just shuffles any characters that are 7-bit only, so you would still have console access.
Mathing a bit here, 7*8 = 56, so 7 bytes of data will fit into 8 console characters (with bit #8 / high bit always set). Let's make the blocksize some multiple of that to make it easy. Maybe 10x it, so a block is 560 characters = 490 bytes.
Add an extra 14 bits of CRC (safety first!), 7 bits of opcode and maybe 42 bits of address field to select the block to read or write (gives about 2000TB addressable? should be enough) and off we go.
TX: [OpCode=0x1(read) | Address=yyyyyy | FrameCRC=xx]
RX: [OpCode=0x2(read-ok) | Address=(same) | DATA*560 | FrameCRC=xx]
TX: [OpCode=0x3(write) | Address=yyyyyy | DATA*560 | FrameCRC=xx]
RX: [OpCode=0x4(write-ok)| Address=(same) | FrameCRC=xx]
TX: [OpCode=0x5(size) | FrameCRC=xx]
RX: [OpCode=0x6(size-ok) | BlockCount=yyyyyy | FrameCRC=xx]
(Any console stuff being multiplexed into the frames would be 7 bits and just get ignored. And if something does go wrong, just wait a bit for the serial line to go quiet and try the command again...)
Perhaps also needs a one-liner patch to the linux tty driver to drop any characters with high bit set, so the kernel does not try and interpret data from the tiny flash pcb as console commands.
(And maybe use an SD card slot instead of a small flash chip if that is cheaper.)
Plug this imaginary device in the console port and Bob's your uncle! much extra flash memory
... 
Why on earth would you do that?