Time to replace the coil packs?

I'll start off with the basics... 1981 KZ1000, rebuilt with parts from a couple different bikes, everything is pretty much original.  The coils were probably weak when I first put it all together, I've always had that gas smell from it running, and it never had a whole lot of power (which is why I'm leaning towards coils here).

Trying to get it going this week for the season, but it's just not happy.  Cranking it so much that it's pumping gas onto the ground so I presume flooding out the cylinders.  It does eventually start but there's very little throttle response.  Cleaned the plugs twice.  Today when I cleaned them, inside right cylinder plug is completely covered in carbon.  If I can get it going long enough to ride up and down the street, it takes a lot to keep it running, and there's backfiring on the right side.  The left side seems better, but still not putting out a lot of heat to suggest that it's really running well.

Another thing today, after cleaning the plugs and getting it to start again...  I can barely keep it running, but then something catches and it jumps up to 3000rpm.  It'll run there for a couple minutes, then choke itself out and die again.

So from my knowledge, this all points to little or no spark.  If anyone has other ideas, let me know?  (Erg it just occurred to me that I should have pulled the cap to check the points.)

And if the coils are indeed the problem, then the question becomes what should I replace it with?  I'm hoping to keep it simple, something that is a straight OEM replacement that can drop right in without having to do any rewiring.  Modern replacements are fine but this is just a street bike so I don't need anything fancy.  If there's something I can snag off Amazon then maybe I can try doing the swap next weekend.