How to choose a cartridge you can't hear on your system?

Great question...the answer is you can't.  The dearth of stores willing to demo cartridges are dwindling, and even if you hear two different cartridges in the store, setup is oh so important (I look askance at all "experts").

Dealers could have at least a few set-ups for auditioning.
Not my problem, though. When and if I am ready to pay thousands  of dollars for a cartridge, I'll make couple of phone calls and get precise advice. You got to have priviledges and connections, then you'll be fine, cartridges or not.

Let me ask a different question.  Can one generalize that a high end cartridge of a manufacturer produce system synergy if their lower end model(s) do?  

I'm curious if it is always a crap shoot or if one could try several "cheaper" models and then commit to their flagship with success.  

I would never do it, this can be a very costly mistake. Besides, many brands don't have anything that I could call 'cheap'. Over $1k is not cheap, at least for most.

I’m not sure how easy this problem--and it is a problem, at least with expensive moving coil cartridges- is to solve. Ideally, a dealer would have a few different cartridges set up, using the same arm and table. But, dealers are typically limited to certain brands. Perhaps a show- but why would a manufacturer bother? (Assuming they took the time to do the necessary set up and demonstration, they are comparing against their competition and I don’t see that happening). Listening to the cartridge in question in someone else’s system --and any system but yours is ’someone else’s’--isn’t going to tell you much- sure, you could swap out cartridges on that system and hear the difference on that system, but it still doesn’t tell you how it synergizes with your set-up.
Didn’t Fremer do some comparisons, digitize them (yeah, I know) and put them up for public evaluation on his site when he had the Continuum table and arm?
I sort of played it safe- used Lyras for many years until my dealer at the time said he thought I’d really like the Airtight. So he brought it over and installed it. I guess if I decided I hated it, he would have taken it back. But I didn’t hate it, I grew to appreciate what it did. And bought the next model when I felt it was time.
But, we are very limited by this process.
Once I get my second system set up with removable headshell, I plan to play around with some less fancy cartridges, some older ones. I think that will be instructive. In the meantime, I soldier on....
PS: there are people whose views I trust. If @AlbertPorter, for example, who uses the Airtight, says the Opus is better than the Supreme by a margin, I take him at his word, even though he uses a different arm, and has an entirely different system than mine.