Sagerat, you said you've used yours as a dual-sport before you got a purpose made one. How bad of an idea would it be to buy the Ural Solo with the intent of using it as a dual-sport? Would a 2wd be better?
I'd go 2WD, myself, instead of the ST. See below for more blatherings on dual sporting with a Ural.
We rode our Urals on USFS roads and well-established two tracks. Here's the deal about a hack off-pavement: your wheels never match up to those of a two track or the tracks in a gravel road (cue Linda Williams) as the width of the hack is so different from other vehicles. The hacks are also rigid mounts, so it feels weird when you are trolling along and suddenly the hack is on the high side of the bike due to the camber of the road/two track or the topography. Normally, you try to keep the bike above the hack, but sometimes that's not possible, so you just scoot your butt over as far as possible toward the hack; I've actually had to sit on the left edge of the hack, which is the side closest to the bike. (The hack wheel and fender are on the right side of the sidecar.) I've also stood on the pegs like you do on a dual sport. Got stuck once and stood on the passenger pegs to power out.
The Urals don't have much engine compression and they weigh ~740 pounds, so on a steep downhill the front can plow instead of turning if you get too much momentum, but you never have to worry about falling. We did climb shallowly sloped banks when a road conked out on us due to deadfall. Shh, don't tell the enviros.
The ST can do gravel roads and probably two track with extreme care. But remember it has no skid plate and the mufflers on both a sidecar and the ST hang pretty low. There are aftermarket high pipes for the sidecars. Think of the ST as either a 1970s airhead Beemer or a UJM or UGM and ride it accordingly. The ST isn't much for ground clearance or fork travel or fender clearance. That said, there are videos on youtube of guys ripping along on USFS roads in the Cascades as well as Death Valley. Mr. COB makes aftermarket clutches for the Urals to handle lots of low-speed abuse.
To get an idea of what a hack can do off-pavement, either go to ADVrider or hit youtube and search for Ural off-road rides or similar terms.
The Urals were amazing for what they'd take into the backcountry what with the hack and its trunk. However, after two seasons of dual sporting, we did all go to KLR's as we could places we wouldn't take the Urals. Urals are not skinny... One buddy has even gone to a TW 200 that he bought for the wife...not that she can ever pry the keys from his hands; even though he's 6'6" he loves that little TW. (I'm waiting to see what happens to the TW now that he has a Rokon, but I digress.)
Sorry for the long-winded reply.