Has anyone got any clever ideas for cutting the wood without removing
the metal?

Not sure if this is useful in your situation...

If you can find a straight path with no screws on the line you want to
cut you might be able to take the door off the hinges and use a cicular
saw (blade at 90deg & depth carfully set an mm or two above the metal!)
with a sawboard as a guide (see http://tinyurl.com/5zys3) then finish
the rest with a floorboard saw or similar.

HTH,

Alex