Re: 1983 Evinrude 15
9.9 and 15 same engine differnt carb, and exhaust and reedplate spacers only IIRC
if the choke is helping then either the carb is still not working or adjusted correctly (maybe try turning out the idle mixture screw till it is about ready to fall out on own... to see if that portion is working), the timing (link and sych) isn't right, or there is additional air entering the engine not through the carb. which leaves crank seals, carb gasket, head, reed cover and case gasket ( where the two come together...very doubtful on that one)
Wish you were in S. cali or arizona I would come by to help you get it running nicely.
I am not saying that you didn't do the link and synch properly just tossing it in as a possibility.
I would likely use some oil, fuel, or carb cleaner.... and shoot it behind carb on outside looking for a change in engine rpm smoothness, then around the reed cover plate, if you are able or willing it might be worth the time should these not work to lift flywheel off and put a good sized daub of grease around crank seal and see if that fixes the issue.
I know if you continue you will eventually find it. I also know that in order to allow a very low idle I intentionally had the spark retarded about 2* more than the traditional link and synch. I'll prob catch some flack for even posting that. but it allowed me to troll with a 12ft john boat that way.
after you run out of common fixes, and free or close to free and simple checks unfortunately things start to get interesting.
one other thought, even though the part is brand new, did you check the orifices anyhow to make sure they didnt have a bit of flashing, plastic... crud in them anyhow. and did you use silicone on any part of the carb?
sean