Here, I will wade into this, nobody has replied in a while, and the other topics are stale.
My thought is, depends on what dirt track frame you use, whether it works well on asphalt or not.
And I think this is worth figuring out, because dirt trackers on asphalt are real fun. I think it was a picture of Snuffy Smith on his Triumph Trackmaster at Road Atlanta in some magazine that got me into AHRMA racing to start with, and I never really considered any class but 750 Sportsman where you could basically race a dirt tracker on asphalt.
I have ridden dirt track frames on road race courses a fair amount over the years, I rode a period, original dirt track Redline 750 Triumph 1992-3 through 2001, and put a modern C&J copy of a Champion under it for another 5 years or so. The Redline frame was not so good, the Champion, thumbs up. In fact, it is up on my stand now being worked on, and I am going to bring it out this year.
I certainly remember the Yamahas David Temple and Johnny Ellis rode, man, David getting a bad start at Sears maybe 95-6? then passing a clump of us on the first lap on the inside under the white line in turn 5, the right before the Carousel, slithering and swapping the whole way, phew, how could I forget that? Johnny's always looked a handful too, but also really fast (I think it was all pilot for both these guys).
Anyway, for asphalt there are dirt track frames, and there are dirt track frames, and not all of them work for this application. Trackmasters, and I hope I don't offend anyone here, aren't necessarily the tip, especially for 750's (interesting Carl has the same problem on his 200), they are real flexible, in fact made to be flexible, the center backbone is not well tied to the tubes from the pivot area to the seat, there are no up tubes connecting the outside of the s/a pivot forward to the back bone, the outside of the swingarm isn't located well, and the pivot bolt and bearings are small, and the flat wheel plates on the swingarm flex too, and the motor mount plates are long and flexible, and not tied to the swingarm pivot directly. Great for dirt track, not so rigid for asphalt. I had a Trackmaster 750 Triumph dirt tracker and it wiggled a fair amount on dirt, couldn't imagine it on asphalt. Funny, true story--first time I met Arty Stapleton, who runs a 750 Trackmaster, at Savannah 1993, his rider Duane Veeder (national number 99 dirt tracker) was parked in the grass outside turn 4, the left at the head of the pits, and he just sat there the rest of the race, didn't get off the bike or move. Later he said it was pumping and swapping so hard after hitting the bumps that used to be on the apex (before it was repaved) he was glad to get it out in the dirt where he knew what to do with it. But Arty's bike has had some real good results, it all depends on the pilot.
My period Redline had the same flex problems. While the Redline had a stiffer Champion style full cradle frame design that held the outside of the s/a pivot, it still had flat axle plates and a little swingarm bolt and s/a bushings, and little thinwall 7/8 tubing and little flexible triple clamps. It flexed a lot, a handful, hard to know where it was going next, but really, really fun. Lively, say.
All I can add to this thread is I changed from the Redline to a modern (NOT period) C&J reproduction of a Champion some years ago, and it is dead steady. The Triumph cases mount outboard in the rear (that allows the rear motor mounts to be two little 2 inch C shaped chromoly plates that mount like big flat washers under the nuts on the swingarm axle and directly to the motormount bosses on the engine cases so the engine pushes directly on the s/a pivot)-- and with the engine so solidly tied in the frame there, and the bottom, and the front, and in a real stout top motor mount, it stiffens things up considerably. The swingarm bolt is big diameter, held in the frame in two boxed plates on each side, with enough diameter in the pivot tube to leave room for a stout spacer between the bearings, so you can tighten it all up, and it pivots in needle bearings. This C&J version of the Champion also has the engine loop and the seat loop made from 1 inch chromoly, not 7/8, so it is quite a bit stiffer, it has a 3/4 chromoly rear axle with outrigger bearings (4 total bearings) and a 1x2 inch chromoly swingarm with sliding axle blocks full width at the axle, and it has 38mm Marzocchis with full thickness Ducati triple clamps too.
So I go slow, and I am getting slower as I get older, but this is a very stable, comfortable dirt tracker to ride on asphalt--it's a lot better than I am. It's all in what you use for a dirt track frame--C&J made this one more like a modern dirt tracker, with a lot more stiffness built in. FWIW.
Road Race 48X
Motocross and Dirt Track 48M