Thanks. That's a possibility I'd considered since my OP and I do have some nicely matching wooden strips from an old louvre door which wouldn't need much doing to them to fit unobtrusively. Gravity would hold the blind in position at the correct height, the only role the wood strips would play would be keeping it nicely parallel to the window so they'd need to be the other side of the blind from the arrangement on your window.
Our windows are 20 years old now and have stood up very well to the elements. They are suffering from the mildew problem on the inside of the frame though and I promised myself I'd clean, sand and retreat them this year. Mind you, I said that last year too...