I'd love to peruse the Merc service manual for your carb, but boatinfo is still down. That sucks as the service manual for the Mercarb is pretty thorough. Here's my take on it.
Carburetors have an adjustable idle mixture, then when you crack the throttle, there are ports built into the venturi which draw fuel into the air flowing past. With the throttle cracked open, the fuel mixture adjustment is set by carburetor design, not by virtue of an adjustment you can change. Once you start getting the butterfly open past maybe 1/8th throttle the main jets begin to come into play and become the most important consideration. If the problem occurs with really early, less than 1/8th throttle opening, then usually a passageway, what I called a port, is possibly plugged or the float height is wrong. I believe that Mercarbs have a power valve as well, which comes into play when the throttle plate is nearing wide open and with high airflow, minimal to low vacuum conditions.
I haven't done much with the 2 barrel Mercarb. I think I would look towards float height first. That plays a huge part of the mid and high range behavior. Then I would consider if the stumble is a lean condition or a rich condition. I would guess lean, but that's all it is is a guess. You might run for a bit with it stumbling then turn the key off without changing throttle position, so you can look at plugs as they look like right then, during the stumble behavior. Pull a plug from one of the middle two holes. If wet then maybe running too rich. If clean dry and light colored, then best guess is lean.
If you are running lean in a mid throttle range (I would think of midrange as quarter to half open), then the cure is float height first, then main jetting change may be in play. From what I understand of Mercarbs, this may be tough as the jets may not be readily available.
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All the above is general carburetor stuff. If only reality was so simple. Add to the above is possible vacuum leaks, engine wear and tear, timing, fuel supply, etc. Like you, I expect when I fix up and tune up my motor, that it should run smoothly as I add throttle. If I had a carburetor problem, a new carburetor should disappear the problem and I should be grooving on the water. When things don't come out like I expect, then I need to review everything one more time.
You my need to write this all up and post in the Mercruiser Repair section again. I would list every part that is new on your motor. What you have done to ensure clean fuel delivery. And the progression of your adjustments and testing. It is going to take a while to write it up completely. I would consider a short video of the stumbling behavior and your comments to the throttle settings when it occurs, if you have that capability. There is a LOT of Mercarb experience on the forums. Use it. And I will help any way you need.
You'll get it. And then it'll be time to fish all over the delta. All cake after figuring it out.
Rick
