I read a great comment somewhere, perhaps here in this forum, regarding considerations for dual sport tire selection.
The comment was, " You never get stuck on the road."
Essentially the guy was saying, no matter how much off road riding you do (assuming you do some), get the most aggressive off road tire that you can be comfortable with. That one time you "don't" get that big pig stuck will make it worth it.
As far as road handling, many of the more aggressive block knobby tires do pretty well on the road. I run Continental TKC80 TwinDuros (40/60 tires) on my KLR650 and Shinko E804/805 Big Block Adventure Tires (40/60) on my DR650. Not recommending; just saying.
I was up in North Carolina with the KLR in early April (freezing my ass off) and ran the Dragon a number of times...very aggressively with the Contis. They did better than okay...they did great!!!!
The one thing to keep in mind is the more aggressive the tire, the worse they are in wet weather conditions, something we deal with quite a bit. Specifically, tight turning and braking. Doesn't mean you can't ride wet roads. It just means slow down more for corners and allow more distance in braking.
The other thing I ran into in NC was snow up on top of the Cherohala. I had no idea how to deal with that stuff, so I turned around. Bummer, that's my favorite road up there.
Also, I ride with Dixie Dual Sports, so next event let's team up. But yer gonna need something better than the 244s. I ran the Devils Creek Discovery Class this year on the Conti's. I'll be getting a set of D606s next year.