Is it likely that American Mathematical Monthly would eventually accept a Filler article if it asks for substantial re-writing? The email with the initial review says the Filler has "some promise" , but says the writing is poor , and asks for detailed revisions for "further consideration". I'm not particularly keen on spending a lot of time re-writing and correcting the pedantic details, if there is a substantial chance of rejection after that revision.
As mathematical journals go, the Monthly is actually quite selective: I believe their acceptance rate is something like 10%.  For the majority of the papers submitted, the answer is a hard "no."  For instance, I have submitted five papers to the Monthly and three of them were accepted.  For the other two, the rejection was very clear -- they sure did not say "some promise" or "further consideration," so when they say that I think they mean it.

The other thing to know about the Monthly is that they are extremely picky about exposition.  They care so much more about that than any other math journal I know.  Just a few hours ago I received a rejection from a prestigious journal, which described my paper as "very nicely written." The point being that they noticed but didn't really care: they want to publish papers with amazing breakthroughs.  The Monthly is not like that: they take the style about as seriously as the content.  And though indeed I think of myself as as strong, experienced writer, all three of my accepted Monthly articles required massive, repeated expository revisions.  They are really tireless: if after five times you haven't gotten it right, they will ask for a sixth revision.  (This is not an exaggeration.)

A "Filler" is of course much shorter than an article: obviously it can be no longer than a page.  The amount of expository work per line is probably going to be higher than just about any other math piece you could write.  You say


  I'm not particularly keen on spending a lot of time re-writing and correcting the pedantic details, if there is a substantial chance of rejection after that revision.


As I said above, I don't think they're stringing you along.  Based on the response you've gotten, I think you should expect that if you pay enough attention to the exposition, they'll probably take it in the end.  Do be aware though that we're talking about lots of work, for something that is not even going to be counted as an academic publication by most.  So if you really do not enjoy the writing process, you may end up feeling that the outlay of time and effort was not worth the reward.