Is it acceptable to write several small papers that contribute to a larger paper?
As you state it, you are probably going to be fine, however, you have a bit of risk. The first is that if the ArXiv papers aren't really "publications", then citing them doesn't really add much to your CV other than a bit of noise. 

The second risk is that a publisher has to agree that your "combined" work is still sufficiently novel to want to actually publish it and that is up to them and not a question that can be answered here. If all the novelty is already "out there" you might have a problem. This is less of an issue in math, of course, which has a preprint culture currently. 

An alternative strategy, that you can use or not, would be to write a good paper with the important results and then put the supplementary material somewhere that it could be found. 

So, ask yourself whether the combined paper is more than the sum of its parts for your reputation. It might be, or not, depending on the results.