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.