1: We ought to have ontological commitment to all and only the entities that are indispensable to our best scientific theories.

I think this is hard to defend. A utility version of truth works perfectly fine - we don't need to have ontological commitment to mathematical entities, so long as we keep using them.

Now, I hold to a correspondence theory of truth, that is, if something is true it corresponds to reality. So, when we say that it is true that “1+1=2”, we must be referring to some fact in reality.

Core problem with your position, and what you need to convince us skeptics of before you can get anywhere. Many people use multiple forms of "truth", and while agreeing that mathematical truths exist, can deny that they are the same as other truths. That is, statements can be true within a mathematical system, but this does not make them true of/in reality, unless the math is mixed with say, empirical forms of truth, e.g. 1+1=2.

anguages have two sorts of statements, right, the ones that are true by virtue of structural validity (all bachelors are not married) and those that are true due to reflection about the world (grass is green). Mathematics doesn’t seem to have any of the second, so it seems to not be a language.

This links up with what I just said. 1+1=2 is an example of the second kind of truth, as "1+1=2" is just as a reflection of reality as "grass is green". We see green grass and we can place two objects together to have a total of two. All languages can have accurate or inaccurate statements about reality, as well as consistent or inconsistent internal cohesion, and be true in these two senses.

Why we don't like the idea of abstract objects existing is that it follows the same kind of bad philosophy that tries to summon god into existence. Both are unobservable, both are only required if you have a very strict and absolute form of truth.