They are not very consistent from the few I've used. The color analyzer sounds like a good idea, but I haven't tried it.
Maybe you would be best served by using a step wedge and figuring out what the real grade is at your common filter values. Then you could do the same on the new enlarger. I use an RH Designs analyser and it works on true contrast grades if you take the time to profile it. So with it I can switch papers easily. Switching light sources would be equally easy except I have one specific to my Ilford head.
I second this approach! This is the only way to do it. Calibrate your enlarger to ISO grades, record your printing data in ISO grades and f/stop timing, and if you move to another setup, calibrate this new setup to ISO grades again, then use your records to print with amazing consistency.