I had this same issue when I bought my 1970 Mirrocraft Titan 15 which came with a 1970 Merc 500 Thunderbolt. Everyone kept telling me to pull the carbs and clean them but being new to boats I was uneasy doing it.
What I ended up doing was to pull the front off the motor, you will have to disconnect the electronic ignition box thingy, starter, etc to get it off but it will give you full access to the carbs.
Then I took tops off the fuel bowls, pulled the jets, tube and other things I could GET out of the carbs without removing the whole carbs and I sprayed the **** out of everything with carb cleaner and put it all back together.
It's like a whole new motor, I cruise around 35~40 on the water now. That was last year and it's still running strong this year. In fact I went out on a large lake yesterday and ran threw two 6 gallon tanks of fuel pulling tubes. Went the weekend before and the weekend before that too! 3 weekends in a row now without any issues. We had gone out about half a dozen times on the lakes and a few 40~50+ mile river runs out to Lake Michigan and back to where we launched in Grand Rapids.
Previous to that it would cut out when I gave it throttle and it got me stuck out on the lake once before I cleaned the carbs. Been 100% reliable ever since other than a small fuel leak from the rotting fuel line but like I said, I just got one of those.
I now feel comfortable with rebuilding the carbs I think. I have a new factory fuel line, two carb rebuild kits, fuel pump rebuild kit and a whole new engine side wiring harness as the factory ones cracked and dry-rotting.
Going to tackle it this weekend I think. Will post TONS of pictures.