1989 Evinrude 50hp

So I've done a lot of little work on this motor, carb rebuild, spark plugs, fuel filter, water pump, new fuel line with primer ball, etc. However it's still acting up. It'll sit and idle in the driveway with muffs on at 1400rpm, but when in the water it tries to idle at 500 rpm and just dies out. I've increased the idle speed in the driveway three times and it still won't idle high enough in the water to keep running. However when I do get it to turn over if I get it into gear quick enough I can give it gas and then it'll stay going. When I try and actually go though, anything over 1/2 throttle, I get surges in power. there's no cut out at a certain rpm or anything like that it just gives me power and then loses it back and forth. Any thoughts here? Oh also while it idles it likes to backfire here and there which drops the rpms way down. I'm a little baffled, but I'm checking for air leaks this evening in the fuel line. Any other thoughts here?

We attempted to do a link and sync and the motor would not even run after we did that. So honestly we just played around with different adjustments trying to get it back to running and went from there. Yes all the parts we replaced were OEM including the carb rebuild kits and thermostat. Maybe I'll try and mess around with that tomorrow, tonight i get to do 5200 on the keel. Yippie! lol

will do

Alright so got some time this evening and played around with it. I'm able to adjust the idle by moving the throttle roller. Found the engine block and water coming out is ice cold even after running for 15-20 minutes. Also, I did replace the thermostat at the beginning of the year. After adjusting the throttle roller we were able to get it to idle very smooth at 1000rpm on muffs. Played with the lean/rich adjustment for idle speed and found the engine did not respond until the screw was completely in and the engine died. Also, when adjusting the throttle roller to increase rpms, around 1500rpms it begins to pop like described before. thoughts?
Thanks

Alright as an update....
Not going to get to run it tonight but more notes from yesterday.
I did disconnect the linkage to test that and forgot to mention it last night. When I do this the motor dies immediately. Also will not start with the blades closed. When making adjustments to the idle jets there is no noticeable difference until they are all the way closed and then the motor just dies. Lastly, I did mention it never seems to heat up, the block is ice cold even after running for 20 minutes or more and so is the water the motor is peeing out. The reason we adjusted the idle speed with the throttle roller was because it would not start with it in the idle position.
Obviously I'm missing something because while it's running and we got it to run a little smoother last night it is not running like it was designed to. However, I'm still lost as to why. When we rebuilt the carbs this winter they were perfectly clean, jets included so I would assume they are working as they should, but the adjustments aren't doing anything so I'm probably wrong lol. Sorry to ramble just trying to give you the best idea of what we've tried with it thus far.

Sounds like a plan, probably get around to it next week after work for a night or two. I'll keep it posted with what I find. Thanks for the help!