If its backfiring you're getting ignition. I'm not familiar enough with factory pn's to tell you what you have. If you don't have an igniter and it is backfiring you likely have a points setup.
Hei is nice but remember that it is slapped together to fit your Yota. If you have had your dizzy out, I would make sure that it is inserted correctly. It sounds like the timing is way off.
Check your points gap
Most hei units I've seen aren't water proof like the stocker Toyota. Hope this gets you started down the right path