deSolve has utilities such as ccSolve to generate compiled code from R, but I am not sure whether it is on CRAN. From benchmark experience, RxODE is faster for most of ODE problems. However it does not have the flexibility of deSolve (does not support several operators such as modulo, ...)
In this shiny contest contribution, the patient simulator runs a compiled code with deSolve. However, as you mentioned, this code was written by hand and for your case, it is not in the scope of "Building model without coding".