Hi Pete,

The fact that it's a common segment on P1, P2 and the master display suggests to me that the problem is in the segment drive area as opposed to a problem in the stobes or BCD input wiring or the BCD to seven segment decoder. 

It's hard too see which version of the master driver you have - but I think most used the IC drive.  If this is the case, and you can tell by the absence of lots of transistors on the master driver then, have a close look at the bank of 7 resistors towards the top left of the master board.  They are just under  where the left hand end of where the P1 display cable plugs in.   These resistors and the 18pin display driver IC (IC9) slightly lower and a bit to the left are the area of interest.

I have seen a picture somewhere - maybe on this site, of a collection of burnt out resistors in this area.  Driver chip IC9 may also be failed - if socketed you could try swapping it over with IC10 to see if the problem moves to the other displays - and if neither of these is faulty  I'd look next at the BCD to seven segment decoder.  Hope this at least gives you a start.
   

I'd say this description would be correct. The MDB looks like the common DX-8000 - The resistor band in the top left hand corner is where you start - It looks like one has been replaced already at some point.

I hope it is not the UDN7180N - These are VERY hard to track down. Should be a resistor - Do you know how to measure the resistance of a resistor ?

They are 10K each - You are looking for R5 - Segment "e".

Maybe take a photo of the upper left hand corner of the display board to confirm.