After some thinking, I have the final solution. I will combine datarebal's trade bodge with my DIY bodge. The trade bodge will keep the gutter in shape, and the DIY bodge will add strength. The marley gutter sits with a tilt. The DIY bodge alone will not be ideal.
As it is plastic gutter, it will have some flexibility - why can you not just push it up or down enough to get to the screws? you only need an inch or two.