I also had the same problem. We finally pulled out the pins holding the chimes and replaced them with much older, brassy ones from an vintage tambourine that had chimes of the same size. It has definitely tamed the volume.
Yes, I did a similar thing to a modern tambo I have, removed about half of the jingles and it cut the volume down quite a bit.
I have a large 16" modern tambo that had way too loud steel jingles. Instead of removing or replacing any, I just used a thin wire to wire 2/3 of the sets together. The wire just wrapped the pairs together, preventing the zils (jingles) from moving so much and banging against each other too wildly. The wired pairs still jingle but at half their former volume. It doesn't look noticeable because the wire is thin. It would definitely sound better with zils of a different metal/shape.
I think in a real minstrel stage/concert hall setting, volume might have been needed more than our typical settings today. I also suspect the older metals had a nicer tone than modern metal zils. I'm a fan of the vintage 'crimped' pie-crust zils found on a few vintage tambos.
I brought a sweet little red 10" vintage tambo to Sweeney Convergence- it's probably from the 30s or so but it looks grimy and old enough to fit into most non-strict settings. It's a handy size and has a nice sound and volume for smaller jams. I made a small skin patch repair to a hole using hide glue. It's missing a couple of zils.
I actually bought my little red tambo with the intention of cracking it apart to get its zils.... but then when it arrived it was so sweet I couldn't bring myself to kill it. So I repaired the little skin wear/hole area and now I love using it, it's got such wonderful old character! :)