Well. Since you asked, you shall receive.
A prolonged training "montage" (really an arc at this point) can help
establish many things in the setting, not to mention that it's a
strong Mary Sue repellant. Also, the characters are learning about the
world along with the reader, so I'm obliged to deliver all the
infodump, but in manageable chunks.
The only real caveat that can crop up is, that during this time, the
larger plot is halted. We assume the worst, alas, the big bad (the
only real threat) was stopped and he cannot return with the help of a
magical kidney stone. This BBEG is no more!
Should I, and if yes, how should I make such prolonged training arc,
without the reader eating his own face off from boredom?
What does this have to do with "Making a prolonged training montage work".
Let's get into specifics, so I'll break down my explanation paragraph by paragraph.
A prolonged training "montage" (really an arc at this point) can help establish many things in the setting, not to mention that it's a strong Mary Sue repellant.
First. Is this a montage or isn't it? If it's an arc, call it an arc. But more to the actual problem. The point of SE is to be able to help more people having sort of similar problems. So, if you contour the question to only fit the narrow situation of your problem, then it's a problem.
Second off. What does this have to do with making a prolonged training montage work? You're explaining it quite clearly, if in your own words, views, and opinions, but what makes this relevant to making a montage of any kind work?
Then comes the 'Mary Sue repellent'(notice the spelling difference). First. Mary Sue isn't just an OP character (otherwise there wouldn't be the need of 'OP'). Mary Sue is a character that distorts the natural order of things for the sake of making the character look better, for whatever reasons.See Overly Sarcastic Productions' Trope Talk about Mary Sue for more details.
Also, the characters are learning about the world along with the reader, so I'm obliged to deliver all the infodump, but in manageable chunks.
I understand making it clear what we're talking about. But first, infodumping is bad no matter what. But then you make wild assertions: "I'm obliged to..." Whycome? Since when do we (writers) follow rules so religiously that 'obliged' becomes a thing?
Speaking purely for myself, I study the guidelines of others so I'll know when I am breaking which 'rule', but I, in no way, shape or form, feel particularly obliged to do anything but tell an interesting tale.
The only real caveat that can crop up is, that during this time, the larger plot is halted.
Another assertion. Are you asking for advice, or trying to give it? And while I may agree that within certain subplots, the larger narrative may be set onto the backburner, does that mean the romantic subplot shouldn't dare be put into a larger narrative? Should romance only be allowed within the confines of the Romance Genre?
We assume the worst, alas, the big bad (the only real threat) was stopped and he cannot return with the help of a magical kidney stone. This BBEG is no more!
While I appreciate the humorous link (and that really is one of my favourite sketches), you offer another assertion. Why would we assume that? Why would we have to? Sure, it can be argued that [insert assertion here], but have you considered [sprinkle in exposition here], or perhaps [happy beeping (courtesy of E-dy from Fallout Las Vegas, Lonesome Road DLC)].
If you want to know how to make something work. Ask: "How do I make this work?" Then, for clarification's sake, add: "This is my specific problem. This is what I've tried. And I'm not sure if the problem is my understanding of the concept, or this isn't meshing with my writing style."
What you do instead?
Should I, and if yes, how should I make such prolonged training arc, without the reader eating his own face off from boredom?
Your opening question is open: how do I make this work?
Your explanation, or expansion of the premise, is then assertion+assertion+humour=HelpMePlease!
Only to round off with (essentially), "Should I do this? If I should, how?"
So, let's try this instead. And compare my framing to yours, and see if this comes over as trying to get people to engage in conversation, while showing what problem I'm having.
You remember that training montage in Rocky? Where they're playing Eye of the Tiger, and this guy is running and training and doing a bunch of other stuff that has nothing to do with his opponent?
What if this wasn't a boxing match, but a supremely evil overlord (TM) or a dark lord (TM)? I mean, if you were to compare that same setup to Luke Skywalker, where he's training, but in the back of your mind the rest of the Galaxy is essentially waiting for him to hurry the hell up!
Can you strike a balance between the two? To give the reader the feeling that the protagonist is training hard to face a supremely dangerous enemy, while not giving the setting (the world around them) the feeling like the hero doesn't care and essentially abandoned them?
How do you make it feel like the underdog of the tale is working hard, but isn't going to suddenly pull a Neo in a matter of weeks (or downloads)?