Still hard to say. Are you checking timing with a light? Verified that TDC marks on the damper and the pointer are still lining up correctly when it's actually at TDC?
The damper rings can slip over time, and the wrong one can be installed, or an engine swap could have taken place making all the original parts fitment questionable.
As far as you know, is this the original engine? In theory it's not, as it should have been a 289 in a '68. But stranger things have happened.
If it's a swap from some other vehicle however, the timing marks might not line up.
Next, what kind of distributor was it that had two wires? Sounds like the new distributor with just one wire is a standard points distributor for a '68?
Unless you know absolutely everything about this rig from long-term first hand experience with it, then the first thing I'd do is verify the casting date and engineering number for the engine. Then verify the firing order by checking compression with a finger over the spark plug holes while you turn the engine over by hand.
If a camshaft was changed at some point in the engine's life to one with a 351 firing order, or if it's a later model 302/5.0 then it might have the 351 firing order right from the factory.
Another question. Was the engine acting up this way before the distributor change? What made you think you needed a new distributor? Nothing wrong with giving a tune-up to an engine with unknown mileage of course, but if it was acting the same before and after the changes, then obviously the parts already changed were not at fault and now might be adding to the mystery.
So a few more details please.
Maybe even start a new thread with "new distributor, new problems" in the title. Or something along those lines. (edit: oops, you did start a new thread! My mistake)
Good luck.
Oh, and welcome to classicbroncos too by the way!
You new to Broncos in general, or just new to the forum?
Either way, welcome.
Paul