Well, here's where I would use my propane set up to artificially feed fuel to the engine to verify that it will start and run. If it does, I would then know without a doubt that I am looking at a fuel starvation issue. But, without this capability we just have to assume that, because the plugs are dry, it's a fuel issue.
Questions to ask are:
Is fuel getting from the tank to the fuel pump? Is the tank vent open and not clogged? No restrictions in the line or clogged fuel filter? Is any air getting in the supply lines due to a split hose or loose, damaged fitting? Is the quick disconnect at the engine case plugged in and latched correctly?
Is the fuel pump delivering fuel to the carbs? If you're sure that fuel is getting to the pump, then you may want to take the line that feeds the carbs off and put it in a container so that you can observe fuel flow while cranking the engine. Please take proper care to prevent a fire if you perform this check.
If the pump is delivering fuel to the carbs and there is fuel present in each float chamber when you crack the drain screw for each one......then it is likely a problem that is common to all carbs.
This could be anything from a choke problem to all three floats being stuck. Again, this is where having the ability to introduce artificial fuel (NOT starting fluid!!!) might be advantageous. But even without it, we know the plugs are dry so it's likely that you're looking at taking them off and properly cleaning them.
It's not always easy to find someone competent to do this. These carbs aren't real complicated but they are difficult to get properly clean.
If you consider doing it yourself I strongly urge you to buy the HONDA MARINE CARBURETION MANUAL, available from Amazon, before you start.
Good luck and don't hesitate to keep asking questions.