Nautique 351 Carburetor Idle Surge and Stall

I have a 98 Air Nautique with the carbureted 351 engine (basically the GT-40 without EFI) that has been running really rough. It had been idling rough for a while, but it started to surge down to almost stalling unless I gave it quite a bit of throttle. It continues to surge down even when running well over 1000 RPMs, but seems to accelerate well and runs great at WOT. Quite a bit of black smoke coming out of the exhaust which would indicate it's running rich or not burning gas. Also, spraying starter fluid into the carb bogs it down more and it stalls so this would seem to confirm it's running rich. It starts great and the choke is open when warm.

Put on new spark plugs, replaced the fuel filter and put in all new gas. I rebuilt the carburetor at the beginning of this summer. It was my first time, but I was very meticulous with a manual and thought I did everything correctly. I put the carb back on the boat and I'm still getting the same problems. I have tried to adjust the idle/air screws per the manual, but they don't seem to have much of an effect on the surging issue and I can't get her to keep idle long enough for them to be effective anyways.

I've checked the plug wires and cleaned the distributor cap, but I haven't done too much more than that. It's got a prestolite breakerless distributor. I haven't been able to check the initial timing because it won't keep idle.

I have some limited mechanical knowledge and have tried to do as much research as possible, but I'm not exactly sure where to look next. I'm sure it's possible that I beefed the carb rebuild so I could try to plug a new carb on it. I'm also planning on checking the fuel pump and fuel pressure. Could it be a distributor/timing problem?

Any other ideas for things I haven't mentioned?

Thanks in advance for any advice! I've read through these forums many times since my mobile mechanic died and it's kept her running for some really good years. Really appreciate the knowledge-base here.

Thanks, KENO. I looked down both the primary and secondary barrels and I didn't see any droplets. Had to give it some throttle up to about 1000 RPM to keep it running so I could look. I'm starting to think that it may be an ignition problem as well. The RPM fluctuations seem to be too consistent for a fuel problem. It basically bounces every half second or so and speeds up as I increase the throttle until it becomes unnoticeable at higher RPMs.

I put in new plugs and I checked all of the plug wires with an in-line test light and they appeared to be blinking rapidly, but didn't look like it was 100% consistent. I ran out of time, but I'm thinking I need to do a more thorough test on the ignition coil and the prestolite breakerless next. Not really sure how to go about diagnosing problems with the prestolite, though. I suppose I could just replace it,

Be on the lookout for a vacuum leak as well. Especially around the base of the carburetor since it was just off. Cook be a gasket issue etc.