IMHO, the NCR and C&O aren't very demanding 'trails' They're unpaved, sure, but pretty gentle as far as curves and grades go. I've ridden the entire C&O, including Harpers Ferry to Georgetown on 32mm slicks, so a '+plus' bike or fatbike would be overkill for anything short of a full washout of the towpath, and they usually re-route the trail for that.
I think your issue with slippery / rough conditions is that your Vaya's based on a road bike, nothing crazy with the geometry, but it does have a road bike's forward weight bias. The more upright, rear bias of an MTB, along with wide, straight bars, even with a 'narrow' 2" tire would do more to improve the handling in those conditions than moto-size tires. A short-travel hardtail or rigid (do those still exist?) would give you the bad-surface performance without the speed and weight penalty of ovesized tires.
I wouldn't go super-agressive with the tires unless you plan on spending most of your time off-piste. I used WTB Raptor F/R's for the clay and loam you find on the other side of the river, but you pay for all that grip with increased rolling resistance on hard-packed surfaces.