a moderately-priced but functional midi organ

We've definitely all been there (and most of us are still there).  Lots of us in the forum have built our own VPO for OTQ (which is basically what you're describing: a Virtual Pipe Organ).  There are a lot of guide videos for building/assembling a VPO.  Personally, I went with two M-Audio Keystation 61 and one Keystation 88.  I also have an Oxygen 49 that sometimes use for "pedals" as my office studio as a composer is *very* cramped.

I love the action of the smaller Oxygens (I think the 88 goes back to having a piano style action), it's the nicest synth-type action I've ever used, and I've played a lot of keyboards, pianos, stage pianos, and organs over the years.  The M-Audio Keystations are usually the go-to cheap option, but there are a variety of alternatives (typically the closest to a true organ is going to be a Fatar-style action but generally decent M-Audio keyboards come quite close--especially considering the ten fold price difference with then the "real thing" being another two to four times more than that, my next choice would be Nektar but I don't regret going with M-Audio which was less at the time).  All of mine are from the used market, where they were a lot more affordable 1-3 years back.  The used market has dried up a bit and now they're running at 2-3x times what I paid for used throughout the market.  I don't know if the market will improve or not in this regard.  If there's a long-term downturn of any significance, people could look to make quick cash on gear with a sudden surge of supply, which could leave the market filled with $30-80 keyboards on any given day, whereas a quick search shows aver $150 plus shipping for used which borders on its MSRP.  Though, there's the consideration of shipping, which will almost always be on top of that when buying used.

Keyboards are always harder to buy from smaller ebay or reverb sellers (as opposed to medium and large chain retailers like Guitar Center or even Walmart/Amazon), as most owners selling them as a one-off will tend to need to arrange for comparatively exorbitant shipping costs and logistics, especially for larger keyboards.  The best bet for used will be sellers that can offer competitive shipping (Guitar Center, etc.) or through local music stores.  Most piano stores will only sell new keyboards (typically hiding them at the back so you have to walk through the entire store of high-end, new or newly refurbished acoustics to help the electric keyboard costs seem more reasonable), and they'll typically only stock piano-oriented keyboards, rather than the more niche organ-oriented ones.  I've done well with local brick-and-mortar music stores, as shipping costs are usually taken care of, as long as they have used stock that matches your needs.  Some local brick and mortar big box stores will carry one or two midi keyboards (Sams Club, Costco, etc.) but they're selection will be extremely limited though likelier to have bulk inventory.

Right now I couldn't begin to tell you whether or not now or in two weeks/two months/two years will be the best time to buy used or new.  If goods costs rise, your project cost will go up proportionately with it.  However, as goods costs rise, demand will decrease and if unemployment and underemployment increase, people will be more inclined to ditch gear for next to nothing.  Large retailers might be left with clearance level prices on perfectly new and fairly recent inventory.  That said, in the US market, most keyboards contain a lot of imported parts (frequently the parts are imported into in an intermediate country, assembled, and then exported again) which makes them much more vulnerable to global trade/supply chain considerations, which could be a lot of why the market is running at or above MSRP for used as of today.

You're going to know best what you need, what you can afford, and what you're comfortable spending immediately as compared to what you might risk spending later (or not).  I would guess that you could buy 3 Nektars today for around $300-350 or 3 Keystations for $525-650 total.  If you wait long enough (and it's anybody's guess how long that would be), you could pick up 3 used Keystations for $175, including shipping.  If you lucked at through FB marketplace or a local music store, you might be $125 or less.  Guitar Center runs bulk used sales occassionally, but shipping is on top of that (though a fairly reasonable flat fee in the $5-20 range depending on keyboard size).  3 Fatar keyboards would be more $4500-12000 (not that worth it in my opinion) and 3 "real thing" keyboards would be $6000-18000, with then a full console running potentially higher than that, depending on a bunch of other factors.  If your budget is in the $500-4500 range, you should also consider local churches may replace their consoles and ditch their old one in that range.  A lot of those will be recent enough to have some MIDI function or be able to be converted for MIDI (for roughly $125 if you do the labor or $500-1000 if you hire that out).  You will need to pay freight or transport a full console home, which is no picnic.

Also, midi drum kit/pad controllers and other midi accessories can easily be used to change stops.  Those tend to run $50-125.  (And more advanced keyboard controllers often have a set of drum pads or buttons that can be programmed and used for changing stops).