List of files containing slave and/or master:

There are a few choices of replacements in the literature, some of which are listed here: https://en.wikipedia.org/wiki/Master/slave_(technology):

primary/replica (perhaps doesn't quite describe the situation for the simultaneous fits)
primary/secondary
provider/consumer (again, maybe not quite right in this situation)
coordinator/worker
conductor/musician

Several others replace the more problematic 'slave' but leave 'master', however I'd prefer to avoid this halfway house.

I think the first 3 you list don't really work very well in this context (as you say). However, 'coordinator/worker' describes rather well the relationship of the objects here.
A few alternatives to replace 'master' along the same lines could be 'manager', 'director', or 'controller'.
But I'm struggling to come up with other good alternatives to 'worker', which could maybe still be taken to be a bit pejorative? Maybe 'runner'? Any other ideas?

I suppose at least 'worker' should imply someone being paid for their services. Maybe 'fitter' could also be an option in this case.

I suppose at least 'worker' should imply someone being paid for their services.

True, it's certainly a massive improvement. And of the alternatives, I think 'manager/worker' is my preferred option at the moment.

Maybe 'fitter' could also be an option in this case.

I don't think 'fitter' works because (to use the current nomenclature) it's actually the 'master' that interfaces with Minuit, while each 'slave' calculates the total NLL for its particular data and model, given the set of parameter values provided by the 'master'. So 'computer' or 'calculator' might be appropriate but they sound a bit odd to me. Maybe in conjunction with 'controller' they could work?

Have switched to coordinator/task as seen in review D35