5hp 4 stroke runs great trolling, dies at mid or hi throttle

I have a 2001 5hp 4stroke I got used. The motor starts first pull and will run all day at trolling speed. If you advance the throttle it will run up smooth for a while then just cut off. Like turning a switch. No sputtering or hesitation. Takes a lot of pulling to get it started, and when restarted, it won't advance much above idle and it will die again. Once it sits it will start right up and act the same. I pulled the fuel line to the carb and verified plenty of gas there. The engine is warm, but not overheated. When I pulled the plug, it's a bit wet, but not at all fouled.
I suspect a bad coil or maybe CDI unit, but at the price for replacements, I don't want to just throw parts at it.
Can anyone help?
Thanks, Sam