This should be no big deal, no need to pump the fuel out of your tank. Seafoam dissolves carbon deposits and it does it very well. The engine is supposed to smoke. That's all the dissolved carbon buildup from your engine being burned away.
What has probably happened here is the seafoam has cleaned out the fuel system and the dissolved solids / carbon are now stuck in the fuel filter and carb jets. These will need to be cleaned out. It's highly unlikely anything at all has been damaged. In fact once you get the fuel filter & carbs cleaned I bet the motor will run better than it has in years.
Pop the plugs out and take a look at them to see if they are fouled. Take a rag and dry them off then use a wire brush and scrub them clean. Be careful not to change the plug gap. If you need to re-gap the plugs start with .030.
I think you hit on the problem. I had major problems with my 9.9 Yami 4 stroke kicker after using Seafoam that may or may not be a coincidence.
The main motor is a large fuei direct injected two stroke and both it and the 4 stroke kicker run off the same large fuel tank although both have their own fuel lines and separate Racor filters. A the end of the season I put several cans of Seafoam into the large tank to clean out the motors and act as fuel stabilizer over the winter. Seafoam did a great job on the fuel injected two stroke, cleaned it right out and a little bit of roughness it had developed went away and it ran beautifully.
Different story on the older Yami 4 stroke however likely because it was carbed. Had a year of hell with it after that the following season. It would foul plugs and make oil like crazy (gas getting into the motor oil). Did some minor work on it ourselves which did not solve the problem and had two different shops work on it, both highly capable and experienced with Yami. Had to pull the boat and change plugs and motor oil repeatedly, not to mention back and fourths to the shops and that is a fair bit of work as it is a full remote with a plumbed in fuel line (not quick release) .
We replaced the plugs, fuel filters on the racors, the fuel filter on the kicker and replaced the fuel pump with the newer water cooled type and replaced the temp sensor. It would run well when plugs were changed for a day or two but then - Same problem.
A yami shop did a compression test (compression excellent) and replaced the idle circuit with a good used one as well as the plugs and motor oil (again). Ran well in their test tank but - Same problem when installed back on the boat.
Took it to another Yami shop with an excellent reputation and they replaced the plugs, temp sensor and fuel filter (again), completely disassembled the motor and cleaned out the exhaust which was clogged up with carbon and gobs of black gunk. It was an expensive bill. It ran well in the test tank as it always did after new plugs but then- same problem after a day or so on the water. This is a very good repair shop which stands behind their work so they said bring it back which I did and they swapped out the carb for another good used one for free and then ran it in the test tank for days. I think they were tired of seeing my smiling face. The problem was finally solved. The old kicker ran like new all last season, stopped making oil and hopefully has a lot of good years left in it.
My theory is that running Seafoam though an old 4 stroke or any old carbed motor, especially those without a standard choke system may not be a good idea as it likely dissolves crap in the carb which was otherwise stable and deposits it in jets and other critical small passages. Especially if that liquefied crap sits in the carb over the winter and drys up although I run the carbed motors dry before the winter layup. Too bad both motors feed off the same fuel tank because Seafoam does do a great job on the big fuel injected two stroke but I am afraid to get it anywhere near the old 4 stroke carbed kicker after that experience.
Now I have a new problem developing with the starting circuit. Likely in the remote unit as when we turn the key sometimes it is as if it is not making any contact and nothing happens. So what could this be? Some possibilities come to mind such as a bad contact in the switch unit or a bad intermittent connection somewhere. Finally the possibility of worn out brushes in the starter motor making intermittent contact. I have seen this happen with car starters and sometimes if your car won’t start you can hit your starter with a wench or a hammer and get those worn down brushes to make one or two more contacts which is often sufficient to get you home or to a shop. So any of you with lots of Yami kicker experience have any suggestions on this one???