OK... I am NOT a mechanic... I am what the tugboat guys call a weekend warrior...but
In my experience with Honda /evinrude /yamaha/ it has Never been the impeller. It is good to have impeller replaced but is down in the leg. Thats where the gear lube and water are separated by gaskets. oil and water hmmm. If your gear oil is milky ....you got water in it. gasket didnt work...type o thing...
I would start by putting a little wire in the pee hole( first take off the rubber tube and blow it out) very delicately do the wire probe. Dont scratch anything... You are looking for salt gunk in there. Go to th library. Get the Honda outboard manual. sign it out for a week. ask the honda guy to give you a blow-up diagram of :
1. the thermostat /manifold housing
2. the impeller housing
3. Price the paper manifold gaskets (2) and get the part numers for manifold gaskets ie : the metal one you can clean with a scraper and reuse(dont scratch it) paper ones you need 2. Price the thermostat. You can always soak in vinegar, but if you go to all that work....spend $58 on new themostat and a few more bucks on gaskets. Then when you know how...just replace gaskets evey 3 yrs. If you flush EVEY time -ten years...There are 8 nuts to take off. You have to take off a lot of linkage. Put them away in seperate plastic sandwich baggies and label. Put em all together somewhere safe.
My guess. Thats what it is.
Have fun .. Listen. I did this on a peice of junk engine that I never did fix about 10 years ago. I felt like a complete failure. I have worked on many outboards but that one got me. ...I did it again with this NICE honda this year and I had such a celebration because I had not failed...it just took me 10 years to use my knowledge on a honda that wasnt a dog.
Besides.. LEARN man ..It is just a machine... If you REALLY need it to work....take it to a mechanic...this a no-brainer for them... but then ya never learn ...If you have time..take the journey..good luck!! Dont take it too serious...