Although in general I like epoxy, I use an exterior Titebond II type of glue for this part of the job. I don’t have to wear gloves with this kind of glue, it’s less slippery than epoxy so the bundle of strips is more manageable, and it won’t bond to the strip of rubber (much). Also, you can unclamp things after an hour and get strips for the next knee clamped.
Spread the glue on both sides of each strip (one side for the first and last strip). Stack the strips up as you wet them out so they don’t dry as you work. I’m doing twelve strips deep here – that’s a lot of surface so work fast.