The following is extracted purely from firmware files and USB logs, from
both Kevin's zip and my upgrade attempts:

remote, arch, fw version, d/l pattern, write pattern

550 9  2.2.3  8xFF  3a8dffff4847ffff

628 7  3.0    4xFF  234d4847

659 7  4.1    4xFF  ad8d4847

670 7  4.1    4xFF  b4de4847

676 7  4.1    4xFF  ee344847

688 7  3.0    4xFF  b8244847

745 ?  1.0    other Just *insert* 0x47 before?

748 3  1.9    4xFF  e4e74847

768 3  1.9    4xFF  83074847

880 8  4.0.13 6xFF  fb85ffff4847

880 8  4.4.2  6xFF  d8f8ffff4847

890 10 4.2    ?     11abffff4847ffff ?
  I haven't quite worked out the download format of this,
  but the USB logs I think I interpreted correctly...

So, I guess the rules are:

Bytes 0,1 == checksum/whatever-it-is

Bytes x,x+1 == 0x48 0x47
  Arch 3,7:    x=2
  Arch 8,9,10: x=4

745 is weird. Was that the first remote?
890 needs more investigation.

Now, if only I could work out what the heck the checksum algorithm is
(watch some Logitech employee be reading this and laughing at its
simplicity:-) I wonder how hard reverse-engineering PIC assembly is.

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