Very short travel minimalist suspension fork for rails-to-trails riding

It sounds like you don't really need a suspension fork. The surfaces and conditions you describe are what gravel bikes are designed for - those don't have suspension forks, they just rely on larger tire volume and lower pressure (compared to road bikes).

Short travel suspension forks do exist, but if your frame is designed for a longer travel fork the required axle-crown length will very likely be longer than that available on a short travel fork. (Obviously the for longer travel the frame head tube needs to be higher to give the wheel somewhere to go when the fork compresses.)

Short travel forks will also be lower end and therefore lack adjustment and will be heavy.

I'd go with a rigid fork if you can find one the correct length. Of course another option is selling the MTB and buying a (used possibly) gravel bike.

Essentially what you are after is a bike with good small bump compliance with no need for travel associated with MTBing. As the frame has a tapered steerer, you have a MTB designed for a fork of 100mm or more travel. The replacement fork will also need to maintain the headset height to maintain bike geometry.

MTB Plus size up to 3" would be ideal as this gives very good small bump compliance and completely adjustable for comfort and performance and have no amount of long travel. 3" tires are equivalent of about a 50mm fork. Put the fattest tire that will fit in the rear triangle. A rigid fork that can handle 3" tires allows you flexibilty with tire sizes. The rear probably won't fit the same width tire, so might as well make the bike a mullet with a 29er on the front (probably easier to find a fork that maintains original geometry.

Another option would be install spacers in the fork (in the existing fork if possible, otherwise anew fork) to give a more progressive spring. This means you can run pressures that give good small bump compliance, without traveling too much. It would give a better bike for the trails you discuss.

Gravel bike forks - such as the Lauf Grit Fork (not a recommendation) provide an alternate to a traditionally fork, combining more traditional tire sizes with low travel suspension. These options are all expensive - you would probably be better buying a gravel bike and selling the existing bike.

As I understand it the GVX is 27.5" compatible

https://www.srsuntour.us/products/gvx-700c?variant=32147701989470

It's 40mm/50mm/60mm with 45mm/46mm/47mm offset, which should be fine for 27.5"

I believe the NCX-E is 44mm offset with 50mm travel (NCX-D has steel stanchions for a bit more weight, as well as a cheaper coil option - the E is air)

https://www.srsuntour.com/products/fork/NCX-E-6268.html

Also fairly nice as such things go - air spring, alloy chassis.

If you hate money then you can spend more of it with an MRP Baxter

https://mrpbike.com/products/baxter

or a Fox AX

https://www.ridefox.com/family.php?m=bike&family=32ax