It might be those transistors, it might be an IC. The good news is that it's unlikely to be the displays themselves, and that the ICs are not hard to get.
Download 'my' HP9810 scheamtic and look at pages 60 and 61. The latter shows the anode (segment) drivers for the displays. Now, in the X register you're missing segments c,d,e (at least). Those all come from sections of U16 (page 61 of the diagrams), so that IC could be faulty (FWIW, I've had these ICs where all sections have failed at once). Use a 'scope or a logic probe to see if the outputs are changing state. If not, change U16, if they are, check the associated transistors (you'll have to trace the tracks to find them). Basically, for each missing segment, check the output of the associated 7403 gate, if that's not toggling, change that 7403, if it is, test the transistor.
I notice you're missing the d segment (the bottom one) from all displays. This might just mean all the drivers have failed, it might also mean they're getting no input. Look at page 60 of the
schematics, you'll see that the segment drive lines are buffered (bottom right corner of the page). See if the output of U17b is changing state. If not, change it.