
The downpipe is completely clear, as far as I can tell what's happening is that with enough water coming down the downpipe at once it stalls at the 80mm attached to the leaf diverter. 99% of the time it works fine, it's only during brief bursts of heavy rain, for example what we had briefly today. It's a nasty rock-and-a-hard-place because without the leaf diverter there's a real risk the drains will block, which will be a lot worse than one gutter overflowing.
This is the whole setup:

Does anyone have any thoughts on this? Firstly, is it likely that that's the actual problem, and then what would fix it? I was thinking some sort of inflow restriction at the top so at least some of the water flows on to the second downpipe further down which can take the extra load, maybe a 90 -> 80 reducer to act as a chokepoint where it enters the downpipe from the guttering? Or something as simple as a piece of timber across the throat of the outlet, maybe a 45x45 H4? An additional concern there is that the wrong sort/shape of thing may impede the flow too much.
Anticipating the inevitable, gumming up the join where the water is coming out with silicone or similar will make it impossible to remove the pipes for maintenance, possibly won't work if the silicone won't hold up to water pressure, and will just move the problem to the next-weakest join, so that's mostly a non-solution.