Hi Team.
I'd like to install a fold-down clothesline to the fence shown below:

It's a colorbond fence which sits on concrete sleepers. The width of the sleepers is 2.4m, and the distance between the edge of each post is approximately 2400mm as well.
I've found a clothesline that I like, and the distance between mounting holes is 2260mm.
Now, I appreciate that while the fence panels themselves will hold the weight of the clothesline, adding a few loads of wet clothes is basically a disaster waiting to happen.
I also don't particularly want to install mounting posts bolted into the concrete slab below either.
What I'm thinking of doing is inserting timber strips - perhaps a 90mm x 22mm decking pine piece into the rail in front of the fence panel, screwing that into the rail, and then screwing the clothesline mounting bracket into the pine.

Any thoughts on whether this will work? I'm worried that although the timber pieces will help hold the clothesline up, the shear forces through them may cause the rails to bend and eventually fail.
I suppose the other alternative is to screw in some framing pine to the posts and then screw the clothesline brackets onto that.
All advice is much appreciated.