Honestly that is true of literally any option except Bodyguard (two to three months in capital and then do what you want) and straight up Research Sabbatical. Even Waystones is researchy but focused only on stuff related to that. So we'd have a lot of adventures and related research but not the type of research I actually want to do.
Loremaster? Too busy unfucking Karaks
Markgraf? Same but for Sylvania
Waystones? Same but for Waystones
I disagree with everything you wrote, but mostly with this. If you're gonna reduce the tasks to flippant "unfucking X," why doesn't this apply to Bodyguard and "unfucking the Empire"? No, we should actually look at the different jobs on offer in more detail than that.
Bodyguard and LaL are most like our current job for Belegar, insofar as "there is a defined task that we get every now and then, and as long as that gets done the rest of our time is to do with as we please." I'm genuinely confused why you think we'd be too busy unfucking Karaks with Loremaster to have free time -- not only do we know that we can get a Research Institute if we stay in K8P and use a Great Deed to found one and convert our wizard actions into research actions, but we've been doing this job within K8P for
years, and our standard (per the rundown in my signature) is to give the job 1-2 personal AP a turn, plus some or all of our minion AP, such that we are able to complete the task successfully, and then use the rest of our time for our personal projects. I see no reason to believe that this standard operating procedure would suddenly be hugely different when we're doing it for other Karaks.
With specific regard to Waystones, it's hard to say anything for certain, but I feel extremely confident that if we go for Waystones, the fact that it is a project with a long-term scope, not presenting imminent risk to lives, and has a lot of pieces that need to be in place before you can tackle the next piece means that there's an upper bound to how much productive time we can spend on the job. Also, given that it's a project to eventually do research, we're almost certain to found a Research Institute and get a bunch of half-actions for that, which lets us progress our personal research more efficiently in parallel with hobnobbing with elves or whatever.
With Sylvania, none of those factors hold. There's no defined task that changes year-to-year, just our remit to "pacify Sylvania," which is a
huge task. We're the ones calling the shots; Roswita is giving us independence and discretion specifically so that she can focus on being the Elector-Countess of Stirland. The problem with
that is that there's no way to accomplish a "good enough for our boss" the way there would be for Loremaster-at-Large and Bodyguard, and there's no way to just shrug and be like "oh well, I can work a little less hard this turn and no real harm will come of it" the way there would be for Waystones, because our job is to kill monsters before they kill people. We
know what the thread is like when it's in "people's lives are counting on this" mode: we go
full workaholic. We did it in Stirland, and we did it in K8P during the run-up to Dum: our time-on-task jumped
dramatically once Belegar assigned us the Dum expedition and we dropped almost all of our side projects and interests. I have zero reason to believe this wouldn't also be true for Markgraf, and that's why I'm hoping we can find a substitute for the Research Institute, so that there's a good reason to not just feed all our time into the flame of "making the world a better place."
tl;dr most free time with Bodyguard and LaL, less with Waystones, least with Markgraf, given thread proclivities.