It's easier at times diagnosing a No Start than a running problem. You mentioned a bumpy road... The float in your carb might be sticking..
You said it takes a few minutes to build up speed to 35mph.. Is your foot buried to the floor? Is the acceleration smooth or is it bucking?
Do you have a cat installed? If you do bang on it and see if it sounds like the catalyst is loose, sometimes they break apart and act like the "potato in the tail pipe".
Buy a cheap vacuum gauge and enough line so you can watch it through the windshield. Make note of the inches it pulls in relation to the tach. Record the data and post..
Oh, while you're at it replace your fuel filter.
1980 CJ5 258 with 4.0 head conversion, TFI ignition upgrade, Offenhauser intake with Holley 390 cfm 4bbl, Dual outlet headers with Single Chamber Flowmasters. Power steering and brake upgrade.