I haven't had a whole lot of experience with actually riding Dnepr sidecars, but I've worked on a few Dneprs and the frames seem beefier and more industrial than their Ural counterparts. The deep Dnepr fenders are also more aesthetically pleasing to me. All the rolled steel bits are thicker as are the tubes that make up the sidecar frame.
My suspicion is that a lot of the negative perception of KMZ machines have to do with the slapped-together grey market exports of the last fifteen years, (a la Yuri of eBay fame) rather than anything inherent to the product. Quite simply, many of the specimens we get on this side of the Atlantic have not gone through any quality control, and have even been rumored to be from QC-rejected stock that was sitting in warehouses destined for scrap.
I don't know how much truth there is in that, but I have a Yuri kit-bike engine sitting in my garage with 40km on the ticker with a worn-out cam follower.
The KMZ factory was producing bikes for the Red Army, and like many Soviet enterprises the best examples rolling off the assembly line were dedicated to that purpose, while the parts with looser tolerances were destined for the domestic consumer market. Somewhere in the middle were the export pieces. In light of that industrial philosophy, I'm not surprised that the grey-market Dnepr bits that end up over here are less than great.
I still tend to think that even a grey-market Dnepr would make a fine starting point for an affordable and reliable outfit if one were to buy it with an eye on a BMW airhead motor conversion. An MT-16 with a meticulous setup and an R75 motor should give a Patrol a very reasonable 2WD challenge at half the price. But I've never done this myself, so it is pure fantasy :)
As Red pointed out, Dauntless Motors would likely be able to replace your Dnepr swingarm setup with one that would fit a BMW wheel for $500 or so, delivered to your door in bolt-on fashion. The option to put a Brembo disc on said wheel is well worth considering. Jay's work is impeccable, and his prices are more than fair considering the meticulous attention to detail and design alike afforded by his products.
My experience tells me that $1500 for a Dnepr sidecar in good condition that needs nothing (good paint, lights, tonneau cover) is a fair price. Less if it is damaged or neglected.
My experience also tells me that the fun you will have after hacking your ride is priceless