For lots of jobs, the ability to input the optimiser state from a previous run would be a massive productivity gain.
The cleanest way to implement it for the user would be as a parameter to mxRun, where you pass in the last fit, and this has in it the state of the optimiser which mxRun pushes into the current optimiser run as a set of start values.
fit = mxRun(model)
#--> returns almost instantly having been started at the optimal location
mxRun(mxModel(model, someChange), fit)
#--> returns quickly having started close