If time is cheap then prioritize the signal path and do a circuit section at a time. Consider how much time it takes to un-screw, pick-up, put-down, unscrew, remove, pickup, pullout, putdown, insert, solder, cut, clean (YES only amateurs do not de-flux), inspect, return, screw, return, screw, etc. all the modules, cards, tools, components, etc. involved and time actually means something. Reducing the number of times the soldering/desoldering tools are touched and maximizing the amount of time they are held is HUGE.
If you have to do it around sessions using the whole desk then you have to fix the squeaky wheels first as you can, as described above. If you can work minus a bucket or a few modules over time then I would say do everything at once as you can afford it, ordering quantities that minimize cost. Make sure you make covers for the empty slots! 1/4" ply or maybe buy some blanks on ebay.
I like to use 1/4" foam board to map each card and the positions/polarity/values of caps. Colorcoded highlighters for the different values will make stuffing real easy. I prefer big so I can look up at the shop wall and stuff away.
Mike