SSH + screen works for this. Or if it’s a cluster the job scheduler, but you usually can’t make this interactive. Personally, I just use VNC on my own lab computers since when you log back in you get the same screen. This solves “getting back to the same process”.
However, for intermediate modifications and saving… what types of problems do you plan on solving? If it’s differential equations, the problem with restarting right now is because JLD has problems with saving functions. Otherwise the DifferentialEquations.jl’s integrator interface with a callback for intermediate saves to JLD would handle this just fine.
If it’s for optimization, you’d need to find a way to save some of the intermediate data. I believe the iterator interfaces which are being worked on in Optim and JuliaML have a way of letting you save and modify state.
But for details in “extract ad hoc information from data structures in memory without restarting”, this is very highly problem dependent and we’d have to know what you’re doing.