gutter advice needed

Plumbing advice needed. On Saturday evening Melbourne had a really big down pour and within a minute my gutter was overflowing from the top. I have the whole roof of the house going to the back which will soon be connected to a water tank. Problem is there's a small walnut tree right up against the house (which will reluctantly be chopped down also). The walnuts fall into the gutter and it blocks. Only 6 walnut will do it. What I want to know is, would it be advisable to use 2 downpipes (ie, 2 x 90mm holes in the gutter)? Firstly I don't think the 90mm hole currently there is quite enough for the potential flow of storm water.
The other thing I want to know is I have gutter guard but I had to remove it because it wasn't working (leaves would block the gutter and rain water would build up on the roof). The slope on the roof is not great...probably about 10 degrees.

Can anyone suggest what I can do? I was thinking of dropping the gutter down further (away from the tin roof and using a piece of flashing to cover the timber beam that it attaches. I have included a few photos. Can people throw suggestions my way? I need help.
Tricks

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