Do both engines have the exact same behavior? That is, do both have problems getting through that 1300 rpm range?
If so, and since both engines ran fine last season, then the problem may NOT be with the engines themselves. It seems highly unlikely to me that both engines would develope the same problem at the same time -- unless you are dealing with a common system that supports both engines (ie, fuel supply system).
I'm thinking that it is most likely that your problem is fuel related rather than electrical. The only thing that I can think of that could cause problems at that one RPM would be a slug of bad gas hitting both engines, causing clogging of the carb's intake filters or internal passages (passages that handle the transition between idling and high speed). But it sounds like you have had your mechanic go through the carbs and believe they are OK. Or maybe you have sediment in your tanks that blocks the suction lines only when the boat transitions from floating to plaining.
As a test to eliminate fuel supply problems, I would try rigging a 6 gallon outboard motor gas tank (or similar portable tank) containing brand new fresh gas directly to the fuel intake on the carb on one of your engines. Put the outboard gas tank as high as you can in your boat so the fuel will gravity flow to the carb. If that engine now gets through that 1300 rpm range without problems, you will have narrowed the problem down to fuel supply problems (junk in tanks, problems with the take suction line, filter problems, air leak into the fuel system, fuel pump problems).
Of course, when rigging up the portable tank for the test, you need to disconnect the permanent fuel line from the carb and temporarily block off the open end of the disconnected line (wooden dowel and hose clamp may work fine for that).
Just for grins, here is a picture of sediment we vacuumed our of our tanks:
Here is the story about our tank cleaning:
Good luck to you, and keep us posted.
Curt in Portland OR
1967 fiberglass 38' Chris Craft Commander Sportfisher with twin 427 CID 300 HP engines.