A 1k bootloader is no real problem, I'm not short of space in flash.
I have just gotten this to build, but it was a struggle. If I remove the -nostdlib LDFLAGS setting it can reference the eeprom routines, but the linker also includes all sorts of .ctor and .bss nonsense.
I finally had to track down the right copy of libc.a, extract the eerd_byte_atmega328p.o and eewr_byte_atmega328p.o
files from the archive and explicitly link them in to get the read/write routines without dragging in all sorts of other nonsense.
Now it is time to see if I can use an Uno to load the bootloader into another Uno (I think I'll see if I can reload the standard bootloader first before I try my new one :-).