The pulse generator just helps get the bike started.
All of those parts are bolted to the hot engine so they will get hot too.
I think you are looking in the wrong place.
You need to be more logical.
If every part of the motorcycle was perfect and it mis fired
I would not think it is the pulse generator.
Get a pulse generator from a bike that runs good and put it in your bike.
I think you would get the same result.
Why don't you tell us more about this bike? Show us a photo.
What kind of exhaust,what kind of intake?
Get a workshop manual so you can test these components.
Do you have a multimeter?
Also check with the DOHC websites for known issues.
If you check Ebay and there are pulse generators for
sale at low prices, it is a clue that they do not fail often.
If they are expensive it means they are needed.
Go get your bike back from the motorcycle shop.
On a Roadstar Adventure.