In principle, yes. In practice, these proposals match the spin curve very well and the bullet cluster not so much. That isn't a knock down argument; the bullet cluster offers oddities for dark matter too. However OP implied that because galactic rotation works without dark matter, and dark matter was first posited to deal with galactic rotation, we don't need dark matter. That's not right.

I find it a bit hard to believe that the mass current calculations for the bullet cluster have even been made. How can I convince myself that they have?

It really depends on your choice of modified gravity. Normal MOND isn't extended to relativity, and your choice of how to do that is going to make some big differences. I found [this](https://arxiv.org/abs/astro-ph/0212293) paper from a pro-mond researcher that found a non-relavistic model couldn't account for the behavior of dense galactic clusters like the bullet cluster, and there are plenty of papers by less sympathetic researchers that agree.

I couldn't find any non proof of concept papers that tested relativistic extensions of MOND for bullet-cluster-esq situations. Those proof of concepts tended to disagree greatly with reality, but thanks to the weird effects of (for instance) mass current models you'd expect to need a pretty accurate simulation to avoid compounding error. It certainly hasn't been ruled out.

That being said, while we haven't ruled out that some super weird interacting effect doesn't cause the apparent mass, we know that under a broad range of DM models the bullet cluster is normal. If you assume that apparent mass shows where actual mass is, pretty much all of the weird behavior goes away. It does suggest that so-called "hot" dark matter is unlikely, but that was indicated by cosmological surveys as well.