Heya nice question - will try to write out some of my basic ways of thinking about it for you..
If budget allows, yes an upgrade to Standard or Pro could allow more room to adjust things more professionally for the space, allow you to learn with more controls to try out. I began with Stage.. or Standard IIRC.. but quickly found it was a pro-grade tool for me and haven't looked back after getting into the Studio Bundle (whatever I paid was taken off the top of the upgrade and it's been probably the best music software experience in my time.)
The K2 mono compatible preset can sound solid but yes, without bells and whistles like heightened EQ etc. but that's probably a great starting point, if you want to use the mono compat. sound in stereo - and try some sweetenings of your own to suite the space and repertoire. I do like the Bechstein DG too thinking it can be flexible for worship music from past to present (just subjectively).
In the technical sense, a mono compatible stereo signal is one which, when collapsed to a mono signal, will adequately or utterly faithfully reproduce both channel's signal in the final single mono one.
If you're going to output to stereo anyway, there's probably a few reasons to use a mono compatible preset - and to an extent most presets are OK in that way tbh.
In theory, it's possible for a strongly 'mono compatible' stereo signal to work well when converted/collapsed to mono - but a lot of stereo signals may exhibit differing levels of flaws when doing so (due to variations in left vs. right levels/EQ/timings of inherent ambient noise like room reflections - many things may make poor mono signals when collapsed, and some may display phasing and can seem to have 'holes' where the 2 sides seem to cancel out the entire signal when made into mono).
Many concern themselves with attaining a certain level of perfection when doing this, but in practice some natural flaws after conversion are not all necessarily bad - and if not entirely necessary for some specific reason, some aberrant fluctuation in the mono may not be noticed by most listeners - and in some genres, esp. contemporary ones, often that kind of 'glitch' may be endearing, esp. when pronounced for effect (or fixed and leaves a kind of novel defect or artistically sculpted effect behind) coupled with other analog noise (like tape grit or vinyl, subtle or otherwise).
With some mic techniques (like Blumlein configuration - but there are others too) you may see some polarity flips and different levels in L/R sides and things which may seem weird - but they have technical basis regarding mono compatibility.
Many musicians may not care too much to switch out and try different kinds of mic arrays provided within Pianoteq's mic panel but in all reality, it is what our own ears prefer which matters - even if you're not following exacting rules about mic pairs and placements - and nothing is genuinely wrong or right really. For example, it's not correct to say 'only Blumlein provides precise mono compatible sound', although, it generally will without fussing.. but in any space it may be a creative project to place mics in various places to see what they pick up (noting, often hearing 1 mic alone can seem like it's a lonely weird drafty sound, but coupled with another supporting mic, the combined signals can give some natural and unique effects - time being the main constraint on finding our own interesting arrays and mixes.)
But it's good to have a selection of well known and trusted mic arrays in Pianoteq, and each gives a good representation of these in real life settings.
It could be so, that you find a fantastic distance to place one virtual mic (seeking a mono sound) in Pianoteq which 'represents' a nice listening position in your audience and this may be good because, for example, if you attenuate or turn off reverb on the preset, your room/space may make it up and make the piano seem more 'in place' etc. A case of 'you have to be there to test things' - but I always encourage people to try things to see what works best for them - just because, unless you have a scientific team and acousticians recommending expensive rebuilds and massive speakers and hardware all over the place, we can often find a simple rig will be actually very good even compared to something incredibly expensive and engineered - and Pianoteq allows miles-wide experimentation - cannot lose trying IMHO.
Whilst it's great to hear piano when part of a crowd in a space, it may also be beneficial to have a 'less than scintillating amazing stereo production', which in some circumstances may get in the way of the voices.. that's presuming people are singing and in closely knit community there and so on. So, it could be the right thing to have a not so wizz-bang piano production which I've noticed can overcrowd 'the message' on stage so to speak.
On the other hand, a clean wide stereo possibly lower volume production piano !might! allow voices to be better heard in the middle? (esp. if those voice mics are mono and not also spread wide to compete with piano/music) But all that's up to you, your FOH etc. in the end based on what works in your space for your goals and how the audience responds could drive which way this goes too.
Currently stereo is still ubiquitous, and mono still useful in recording I find (mono piano can be great/manageable for mixing with other tracks, esp. if a wide stereo field isn't a goal of the production).
I'm kind of interested to see what happens with Dolby Atmos though (honestly seems to solve some issues I've been dissatisfied with in other specs.), for high end classical recordings esp. - it seems possible to do well in that space - and even with high-end classical piano being a candidate for representing 'the stage' for audiences and of course multi-media using wonderful tools like Pianoteq, it may be a few short years before consumers are demanding to hear a lot more end products (streams/MP3 etc.) and stage FOH systems deploying Atmos. But that's an aside for now - I'm still feeling that's interesting but could also just be a last gasp thing lately... and it could evaporate quickly too, esp. if consumers just decide "Nope too many new expenses for extra speakers for the best experience and then how much extra do I pay for the streams? Meh.". Really feels a bit either way to me.. which may amount to even up to another 5 to 10 yrs before it goes beyond cinemas and specialist environments.. but a theatre or stage would be ideal whether the public buys in for home use.
But no need for that to stop us enjoying mono piano - I actually really like the way it can sound. But, filling an auditorium/stage etc. will often come down to being 'in stereo' as a preference currently - so while good to try out mono piano, don't allow that to stop you also working out how to make your stage system playback in stereo too in time - beyond Blumlein pair arrays and others in Pianoteq, there are almost infinite ways to move mics around until you hear 'the best sound evaaar!'
Anyway just some ideas as I think of them - hope some of it helps and touches enough on your questions and goals there.
Link gas:
About Blumlein Pair microphone array at Wikipedia
About Alan Dower Blumlein at Wikipedia
Note: Alan Blumlein practically invented the modern concept of stereo reproduction for audio, first patent in 1931 - went on as a force to found what later became EMI etc.
Pianoteq Studio Bundle (Pro plus all instruments) - Kawai MP11 digital piano - Yamaha HS8 monitors