If your goal is to knock time off of your commute, then I don’t think the mtb makes a lot of sense.
Bottom line is that what works best on single-track and what works best on the road are very different and largely at odds with each other.
A gravel or “all road” bike will work very well for your commute (especially if it has rack/fender mounts), and will handle dirt paths OK. But actual single track? You’ll survive, but it is really out of its element.
I think you are going to have to choose which end of things is more important, your road/gravel commute and smooth pathways, or singletrack. Seeing as you are spending 30 miles a day on the road, it seems to me like a gravel bike (with some large slicks), is the way to go.