I was hoping you would get better news and it would be something simple. But at least now you know what the problem is.
Since you are going to replace it, unless you can find one in excellent condition and know the history, I would go with a new one if you can afford it. Jets are usually run hard often hitting bottom and clogging up cooling passages and are usually run in the higher rpm range through most of their life. Most of the used ones were put on underpowered boats and upgraded to a bigger size later shortening their usable life as you have found out. If a used one is very new and well taken care of they usually want a pemium price which is not far from new.
Don't know which way your going, but a Yamaha 115 Fourstroke weighs 402 according to their website. The new Mercury 115 Fourstroke weighs according to the site 317, but it has moved around I think it weighs more, the prop version weighs 359 so I would guess it weighs around 340.
I have heard good reviews with this new design. With either option you get a 3 yr warranty for peace of mind and with a promotion you can usually get a 5 yr and can extend it to 7 yrs.
A 115 Fourstroke should jump that boat on plane in about a boat length and get between 35-38 mph. You will be able to cruise about 2/3 throttle easily and it will sip fuel and be quiet running.
My choice would be the new route and you can get financing on them if you need to. I bought my first one used and the other 2 new. Buying new I know it was broke in correctly and well taken care of. If you decide to get a new one follow the break-in schedule by the book, explains it in the manual.
Just my .02 worth, give you something to think about. I ran my Mercury 115 Fourstroke for 11 years, so if you have any more questions ask away.
Keep us updated on whatever you decide.