As the others suggested, I'd just drop the bowls and maybe touch the float needle a few times to see taht no bits of rubber fuel line have gotten stuck in the needle seat area, and to clean out the bowls of anything that isn't fuel.
As for putting up my engines over the winter here (motorcycles, lawnmowers, woodsplitters...) I change the oil and then always fill up the fuel tank after putting in approx 2X the minimum amount per gallon of Marine Formula Sta-Bil (don't think that you have this brand product across the pond, but there must be something similar). I run the engine enough to ensure that I've got the fuel&additive through the carbs, then I shut off the engine, drain the fuel lines and carb bowls, and leave them be until it is time to start them up again. So far, I've had very good success with things working well when it is time to fire them up in the springtime. These engines sit like this for anywhere from 3-5 months. Sometimes I do pour in some SeaFoam fuel additive too, but I've found that the marine grade StaBil works quite well.