I've had good luck with 2 smokers. Here's what I'd do. Loose order. I work on my own stuff so I tend to spend more time troubleshooting/cleaning before throwing parts at it.
With the motor warmed up set the idle somewhere close to 900 RPM in the driveway on muffs. It will idle 150-200 RPM lower in the water, looking for about 750. Can set in the water too.
Spark test all cylinders to make sure they are firing.
(Verify no change before moving forward)
Compression check first to make sure its worth spending money on.
Then carb kits, fuel pump rebuild kits, and all new fuel lines. Inspect the bleed hoses also. You may not even needs the kits, just be careful with the gaskets, and be sure to set the floats right. Good point above on the crappy plastic bowls. Seal-All is a great band aid for that.
Often times carbs get blamed for electrical issues. That doesn't sound like the issue here to me, but its difficult to say without having hands on. Just be mindful of that. Easy to go down the wrong rabbit hole.