Your calculations just rely on a dozen of data points. You won't need a symbolic "exact" solution for those ellptic integrals. You may set them up as normal definite integrals (which they are anyway) and evaluate them numerically or use them in a solve block, whatever may be applicable. If you are interested I am sure you will find some examples in this forum, most/all of them in "real" Mathcad format (MC15 and below) "only", though. I vaguely remember a quite comprehensice sheet by Alvaro Díaz but wasn't able to find it with a quick search.
Anyway, if your empiric formulas give satisfactory results (at least a somewhat continuous Q.out()), you may as good stay with them, I guess.