Unfortunately, as you well know, every situation is different enough to present unique challenges. Have not recorded at a medieval fair but done a fair amount of field recording (including low rent actual indie film) in similar situations.
In some circumstances M/S recording (and variations) can help . . . but becomes less practical the broader the sound field one needs to capture. Thus not all that useful on then entire choir (as far as helping the NR) but can be helpful close mic'ing a soloist.
Stereo mic'ing a mono (soloist) might well require more gear and or hands then practical, but close mic'ing the soloists can still help with reducing ambient artifacts & intrusions
As the choir will have a general back ground ambient hum it is not particularly difficult to capture a 'sample' of that and judiciously add a bit to keep solo consistent with 'non solo'd' (and in fact solo's might not need the blend at all)
if the client expectation is for a recording as clean as one tracked at a major commercial studio choir room, they probably need to be encouraged to adjust expectations. Ambient can be an element of charm to a field recording, though getting a armorer to keep time with music can be difficult
one of my more difficult tasks, when doing school competitions (more jazz bands then choirs) in typically atrocious acoustic venues was to try to convince band directors that more mics was not necessarily the way to go.
but judicious use of individual solo mics can be useful when creating the finished mix.
Additionally noise reduction, in post, does not have to applied to the entire file as a one shot process. Always depending on performance unique variables at times it is possible to remove the milli sec. of the most offending transients without severe damage to the perfermance as a whole. Different software packages do implement NR in different ways. While I find Audition to be sufficient for a lot of material that only needs light application, though typically I will use more then one pass with relatively high ratios of Noise retained (almost never do 100% NR with any algorithm, in AA typically closer to 30% sometimes crowding 50%, i.e. leaving 50-70% of the noise, with NR less is always more) And unless economic constraints absolute constrain the effort NR is typically most effective when using the smallest possible sample size (not noise sample but applying to smallest section of music possible) And what started this section was the idea that two different . . . typically for me they AA & Ozone, or I gues Izotope's RX . . . NR approaches can be beneficial. Even if I only use AA running too light passes with different FFT 'windows' typically helps . . . different windowing effects which artifacts (NR) show up. And no matter the scheme artifacts are inevitable, trade off is how much noise is acceptable vs. NR artifacts. Then for egregious but isolated noise intrusions of relatively short duration (perhaps even the air horn . . . depends on where it shows up with relation to program) there is old school dolby-esque compression-expansion, here no preset ever works but things like Auditions dynamics processor in edit view are quite useful for accurate control of parameters, including being able to limit dynamics by frequency. This coupled with frequency space editing can be compellingly helpful.
If this is to be a steady gig (repeated annually, bi-annually, etc.) examining whether some form of gobo might be useful might be a profitable study. Again the trade off is more expense, more gear, more cargo capacity for gear, greater set up time, more complicated sound checks vs. level of improvement in end product. A couple of years ago I was relatively surprised when a band director got the schools shop class to invest in construction of gobos whose use would be limited to his band's limited recording sessions . . . recorded them a couple more times, sometimes they were a help sometimes pretty much merely a pain in the ass.
But the idea of developing a one size fits all mobile recording rig that fits into a laptop case or even a single 8 space ata rack case has eluded me . . . of course I came closest to that at beginning of the effort with mono cassette recorder . . .
good luck