I've never understood why we can't have both un-timed and time sensitive missions in game. Way back we used have much shorter ship based missions, can't really remember how long? An hour or two maybe? It gave a logistical consideration to taking multiple missions I enjoyed.
Obviously this isn't ideal for some players with limited playtime, so they got removed entirely...
I'd go along with this too, some short, some long gives you a choice, depending on how much time you have to play each day or week and perhaps scaling rewards adds some depth to that too? A timer that effectively stops on mission completion, ie. 2 hours to complete mission, a week to hand it in adds a third variety too, while also allowing mission caches to clear.
I'm not sure if EDO BGS ticks happen on the same timing as usual but there's a limit to the number of missions you can carry already, so can't help thinking that also limits the damage you could do by artificially storing missions to drop on a certain tick. If that's an issue perhaps the mission stack could be reduced to compensate. I think it's 20 at the moment? That's quite high I think, 10 wouldn't seem overly restrictive to me.