After a visit from the good idea fairy [*] I think I've found a partial solution: The outwards-facing parts of the timber, which get the most direct sun, aren't really visible because they're, well, outwards facing. So I can paint them with high-protection-level house paint and only stain the visible inwards-facing portions, which coincidentally don't get much direct sun. Also coincidentally they're easily accessible for re-coating, which the outwards-facing areas aren't due to the palings being in the way.

 

 

[*] The good idea fairy: