Best way to connect multiple strips?

I am using a Kikkerland 15 and the strips that come with them. Rather, I'm on my third K15 because I keep stripping out the small gear. I'm preparing some strips to go with the box as a Christmas present and some are running longer than the ~13 measures on the printed strips. That's where I ran into trouble - I know now not to overlap the two strips, because that's the place where the gears jammed on my second K15. But how best to connect them? I'm afraid of even using too much tape and I really don't want to ruin this box too.

For future melodies - because eventually I'll run out of the strips I have - I have some 110-lb (199 gsm) cardstock. Is that too thick? Not thick enough?

I have really enjoyed this project - using some existing melodies here on the site, but also charting other songs, transposing, fitting to the two octaves of the K15, and turning into a real physical thing. Thanks for this lovely community.