First thing to pay attention is to try doing quest from the highest rank available otherwise it will take longe.
Courier is one of the fastest and simpler,just do the latest frontline suport available.
Pioneer requires more work, i would do the latest clear the way available, but you just to have some of them active at any time, and eventually they will be completed while you run across ulbuka.
Mummer is terrible, lost article is bad and behaviour research isnt that much good either. This one you probably need to suck it up, take some time to do it and spam till you can get to probationer, where things gets a lot better with morale boosting quests. Then, just spam the latest morale boosting, that are quite simple and fast.
Inventor is cake, maybe there will be some problem to find materials on AH depending on your server, but a good coaltion to do when you dont have much time.
Peacekeeper can be done in tandem, by killing both a colo and a lair reives, with pioneer quests so that makes 2 bird for a stone.
Scouts is kinda of similar to mummer as you have to suck it up with the ergon locus quests, but that is less annoying than mummers quests, and as soon as you get contributor, you have access to analyse, thats like inventors assigment but with less materials. Currently thats what i do to grab fast bayld, just trade one chunk of vanadium ore for 13k exp/bayld.
Also remember you can always just store imprimateur in a coalition in case you just dont feel like doing those at said day, then when you have more free time, like a weekend, you can resume those. Just remember to make sure to have enough space to get back imprimateur from a coalition in case you want to use it in another quest. If you cancel a quest with 15 imprimateurs on you, all extra will be lost.