Stall at idle - wont start

1981 Ski Nautique - This past weekend got out on the water for the first time this year... Here is what happened.
Ran at varying speeds for approximately 45 minutes straight. Throttled back, way high idle about 1400 rpms. It started to do this toward the end of last season. Manually wiggled the carb linkage (secondaries??) and it would return to a more normal idle.
Time for the 9 yr old to wakeboard. After three short runs and idling while he got his feet back in the boots, engine just quit. Turn the key, engine would turn, absolutely no combustion. Took the flame arrestor off and pulled back the throttle. Fuel squirted into the carb. Tried again several more times. Nothing.
Sat for about 10 minutes turned the key and got combustion. Gave it some throttle and it fired. Drove back to the dock and idled while waiting for the trailer. Idle was very rough, stalled again and wouldnt start same thing again. I touched the coil and it was extremely hot. Could not touch for more than a second. No smell of fuel at all. No smoke out of the exhaust when it did start.

On Sunday I cleaned up the wiring to the resistor and took some electrical readings. Included is a photo of the resistor.

Battery = 12.1v
Key switch (off) = 12.13v red to red/w black to black
Key switch (run) = 11.57v red to red/w black to black
Coil terminals = 4.27v
Resistor (key to run) = 3.87v

I took the boat back out for a test run. The carb still idled high and rough. The coil remained much cooler for most of the test run until the end. It got hotter that heck. Could not touch. The battery meter reading while running at about 1500 rpm was 13.53v. One other note. Used two cans of seafoam and filled the tank with 93 octane.

So here are my questions:

1) Is this a carb issue?
2) Is this a coil/resistor issue?
3) Is this the correct coil? SkiDim shows a different resistor.
4) What else am I overlooking?

Thanks in advance for all of your help!

I forgot to mention that I took that photo more to identify the resistor. It was originally connected. It had electrical tape wrapped around the connections. I cleaned up the wires and reconnected. I have had the boat 5 years with really no issues of this nature. I ran a new ground to the dash which fixed the gauge flicker. Other than that it has been very easy to operate.

Ignition aside,

Idle stop is set up too high, likely in response to clogged primary idle fuel orifices.
This loostens the return rod on the secondaries, causing a high idle after a high speed run becuase the secondaries stay cracked open causing a vacuum leak.
Usually goes away with stop/restart.

Best to ultrasonic the metering block and look into correcting the fuel filtering.