Yeah, the cyna is meant to be used with 5 ohm coils. As he installed the Dyna S, I assume he had points so if everything is stock, then the coils are 5 ohm with copper ht wire. Plug caps seem standard at 5k ohms.
As for the dyna being warm, it is next to a hot engine. So it will get warm. How warm I don't know. If I had concerns, I would contact dyna and find out the heat range and then use laser temp meter and check it.
What color are the plugs? A test you can try would be to pull the choke knob partway out and see if the symptoms go away. If they do, then more tuning is needed. If not, it is likely somewhere else.
As a final last resort, while I and many others have had luck with the S, if it just won't work try to get it returned as faulty. Then get the Pamco ignition. Not as well known but they have been around for years and are a very good system. It is what I would get now if I needed a new unit.
The ride IS the adventure. The destination is just to get gas!