I think it could be an option to screw and glue the strips but the ones I glued to my bilge rails have adhered very well so I wouldn’t see any need to screw them as well. The main reason I went for the beta strips is that it didn’t require drilling any holes.
But I guess you are in a slightly different situation replacing the full keel length in that you already have holes to either reuse or seal if not being used and any banding on the keel may be subject to greater abrasion/impacts than the bilge rails are. Perhaps it would be an option to initally just glue the strips and then see how it goes.
Interested to hear how you get on.