Smashing reply Flip. If we had house points on here then that would deserve one..
Billbo, have you ever caught the contents of the float bowls when you drain them?
If not it might be a useful exercise, if it is possible.
What usually comes out of troublesome carbs is little globules of water and/or particles of reddish brown grit.
If you have contamination of this kind on such a repeated basis, it is probably coming out of the tank. Therefore a good rinse out of the tank and flush through of the pipes could do some good.
Unfortunately if you discover that the tank is very rusty inside it might not be just a simple matter of a rinse! But it will certainly help in the short term.
However, water and dirt entering the carbs usually manifests as poor running and cutting out after it has started and the dirty fuel has flowed.
It would be very coincidental if the bowls collected just enough dirt or water to prevent starting whilst running well each time before you switched off.
Looking at the problem from another angle. I wonder if maybe the fuel tap is not shutting off the petrol when stopped and causing the carbs to flood.. This scenario would require leaky float valves too, but it would explain why you can start after draining.
If this turns out to be the case then there is a danger of fuel running down into the bores and then entering the crankcases when standing.
Does you oil level rise? Does it smell of petrol in the oil filler hole?