Excellent question. I've been trying to convert my Triumph TR6R Tiger into a TR6C. I'm also working on a Triumph Cub converting it back from trials to street use. Want to know why? The street, even the worst cracked and buggered concrete we have around here is way smoother than dirt. The problem with the old Triumphs and your Sportster fits in with them is the shocks. They are made for street cruising and compress all of about 3". Take a look at any offroad machine made today and you will find the minimum shock travel on dual-sport bikes is still over 5", with serious shocks springing closer to 8" and on up MX bikes of 10".
So, you get tall saddle heights and lots of springing. That level of shock movement sucks on the street at any sort of fun lean angles at speed. In other words you can't have both. If your off road riding is smooth fire lanes and soft grass with no hidden ripples or rocks you may get away with 4 to 5 inches of shock travel just fine. For that there are some cheap shocks available, which I would try first to see if you still want to do this. The Brit bikes use HJ or JP or something like that. Check the catalogs - there are several. Works Performance shocks aren't too expensive.
Next, don't expect a lot out of your swingarm - no MX jumps etc. without some major work there. The front shocks can be replaced too, but you may just need to swap stock for stiffer springs and let it go at that.
What about upswept pipes and spark arrester mufflers? Also a Sportster ways a half a ton - not the best platform for offroading. And tires. Trials are an OK compromise or Dunlop K70s or Bridgestone ??
Finally, learn to ride the bike on the pegs. That's the best improvement you can make.
You can't just get a Kawasaki KLR650 or Suzuki DRZ?
