Multiple tubes

I have three SBM20s in stock, plus a couple of homebuilt counters. My plan is to connect all three tubes in one counter, am I correct in thinking each tube should have its own limiting resisto?

Yes, you're right. During the discharge of one tube, the voltage drops around 70V. If other tubes are connected in parallel, they will be in shortcut as well, so unable to detect anything until recovery of the one triggered. So they must be powered independently by their own limiting resistor. Ideally, the first part of the detection circuit should also be tripled...

Should be simple on my counters then, only an extra three of four components for each tube.

Perfect.
Just another point to consider: if high counting rate is expected, then check if HV section is able to supply the average current increase (HV voltage before the limiting resistor should not drop outside the plateau voltage limits for SBM20.