fm's library is one of the most complete, flexible, and one of the fastest libraries out there.
(I'm the author of the SR2W code)
fm's SR device interface class can use 2 wire or 3 wire mode.
I'm assuming that since you said:
Now I've had to use another 3 pins for this, so I'm up to 6
that you are running in 3 wire mode.
In 3 wire mode you can "cheat" and share the clock and data pins.
You must have a separate strobe/latch pin for each shift register.
It works because while all the shift registers will be clocking in and shifting new data,
only the one that gets latched will actually modify the data that the LCD is seeing.
You can either run SR in 3 wire mode or use SR3W.
So when working in 3 wire mode, you will
need 2+N pins and N shift registers to talk to N LCDs.
So 2 LCDs would use 4 pins and 3 LCDs would use 5 pins etc...
You also can do the same using 2 wire mode with either SR in two wire mode or using SR2W.
For that you share the clock pins on all the Shift registers but have a separate data pin for each.
So for 2 wire mode you need
1+N pins and N shift registers to talk to N LCDs.
So 2 LCDs would use 3 pins and 3 LCDs would use 4 pins etc...
If you are running SR in 3 wire mode, you should be able to quickly change things to work with
Change the constructors to share the same srdata and srclock pins and then re-wire
your shift registers to match.
You will need to make sure your circuit doesn't use lengthy wires
and to make sure your 595s have proper decoupling to prevent any noise and crosstalk
between the ICs.