more precisely, each server is prng, but has it's own prng seed. maybe a reroll button just would need to ask a different server?
i think the problem is more image damaging than technical. a reroll button would be a neon sign announcing how daft the system is. the missions are ok. the problem is players want to stack them to maximize, or pick and choose. the way to achieve that is relogging. the fundamental error was frontier indulging with this, that's exactly what makes the whole system daft and was the beginning of the mission rabbit hole.
a possible solution (if i remember correctly this was actually mentioned by frontier) would be to disable mission refresh, that is, make all seeds server and mode independent. so you would get always the same missions depending solely on current time and station/system status, relogging would be pointless.
looks like a good solution to me but i am afraid it will meet a considerable opposition, since folks are already used to the rerolls (and rightly so because the whole game seems based on that concept and even encourages it). so i think it should come hand in hand with some thorough mission rewards balancing (and very specially the (silly) collectibles known as mats).
personally, i would also disable mission stacking altogether (could settle for 1 mission per station, with some low max total). shoot me.