Seeding ensemble problems

I have been going through the code & documentation of JumpProcesses in order to find out how to set up reproducible (RNG seeded) ensemble runs. The following snippet yields the same output each time, as intended:

jprob::JumpProblem
eprob = EnsembleProblem(jprob)
    
solve(eprob, SSAStepper(), EnsembleSerial(); trajectories=10, seed=42)

If I replace EnsembleSerial by EnsembleThreads, the outputs stop being reproducible.

I am aware that JumpProblem seems to have an rng field, so one naive solution would be to use the prob_func argument to EnsembleProblem and remake the jump problem with a different seed for each trajectory. That is not directly possible since remake does not accept a seed or rng argument, so I currently recreate the JumpProblem from scratch (which is less than ideal).

There might be a solution to this online, but I haven't found anything, which seems surprising. Is there any better (intended) way of doing this?

Start with the JumpProblem and EnsembleProblem APIs and run the supplied EnsembleSerial and EnsembleThreads solve calls with seed=42. Trace how rng and seed are handled for threaded trajectories; done means either reproducible threaded outputs through the intended interface or a documented, tested explanation of the limitation.