Once the front is weighted I don't think a moto x tire would stop it from ploughing away.
The bike is to heavy to change direction quickly or flick around on the throttle like a dirt bike, might as well send it a letter if you want to try & get out of a muddy rut.
The TDM handles trails remarkably well when you pick a line & stick to it, head up, stood up, legs bent, looking for your next position on the trail. The moment you look down or at the rut you want to avoid it turns to custard. Steps, pot holes & wash outs which make you go eek don't faze the bike if you get your weight right back & keep a bit of gas on, not to quick, though.... With good timing and a good bounce of the suspension getting the front lifted over steps or gullies is possible.
If you know how to ride a dirt bike standing up in tight, slippery stuff the same techniques work on the TDM, moving your weight out of a turn to find traction or in to lose it and tighten your turn, weight back, legs bent over bumps, weight forward over the bars when braking etc.
Sitting on it like a pudding the bike feels awful, all that weight swaying around. It's good on open gravel roads but as soon as things tighten up or get bumpy I'm standing.
My old dual purpose tires were a Pirelli MT 90 front & Shinko 705 rear. Loved the Pirelli, great on wet & dry seal & predictable on everything except wet grass, slick clay & ice rinks.
The Shinko was great value, behaved impeccably on dry tar seal until 2/3rds worn, had a couple of twitches in the rain probably due to diesel or oil. Worked great on trails at road pressure, even better with a few psi let out of it. Not a lot of edge grip through corners off seal but I quite like being able to get around a corner on blips of the throttle so the bike stays upright, especially down hill when you don't want to load the front.
Overall the dual purpose tires increase your safety margins not speed or agility.
I'm doing exactly the same rides on T30 sport touring tires with no problems apart from some downhill butt puckery on wet clay or deep gravel. Get that rear brake lever exactly where you want it.