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Fair enough, in which case I'd go for a solution like @lynx suggested. Find a piece of timber that's wide enough to fit the bracket onto (and hopefully no deeper than the archtrave; plane/cut a rebate along the back top edge so that the bottom corner of the coving will fit into it; screw that to the wall (very firmly) then screw the brackets to that.
ffm-
Screw the bracket to that, or through that into the wall?
I've had a proper look at the pole and instructions now, and only one bracket will need to be on that wall, the other four are on the sides which has no obstacles.
Also, although the bracket base is too big for the gap, the screw holes will all be inside it, which means I just need the wood to act as a kind of spacer to make the bracket flush. With that in mind, I might try and go straight through the wood into the wall.
tbc
Tried that. The problem is that the gap is small rather than the curtain pole having particularly large brackets.
The second problem is finding decent, affordable curtain poles for square bay windows - I can't really be too picky.