Stop TinyMCE from applying styles
I had the same issue with CKEditor. the h1,h2,h3,h4,h5,p tags and color picker were available to the user But we wanted every available tag to has a custom color. To do so I put the CKEditor output which was body inside a DIV with some ID,say node-body-wrapper, then added styles like this

#node-body-wrapper h1{
     color : red !important;
} 

...


In this way I solved the problem. I recommend you to do the same.