I don’t think there is enough rail to take the amount I need: glass to back of the rail is currently ~14mm and then thinnest sealed units I’ve seen without getting silly ££s are 10-12mm.
If you got a ~14mm glass could the beading be mounted slightly differently (holding the glass in from the front face , + you get to choose any mouldings)
It looks like a complicated door. thinking for a second more , if it's even applicable, I'd stay with the 10-12mm glass and set it in with putty (along with the differently mounted beading)
You should just be able to plane down the rails or whatever the name is for the parts which you have to remove to get the old glass out.