Continuing along in the process, this is what I've been up to:
I tried using the Weldwood contact cement as its instructions describe, which did not work at all. The rubber didn't want to stick to itself in the least. I then tried it by just applying it to both sides and clamping it together for 15 minutes. That worked relatively well, but when I added my body weight to the bond to stretch it, the bond broke almost immediately. I mean, the instructions to say that it is not to be used for high-stress bonds...
Checklist
Frame completed
Informative seam tests
Working on:
Making the rubber sack for the interior of the chair via sewing and gooing
Making sure the sack is water-tight
Finding a way to cover the pointy bits inside the chair to prevent ripping
To do:
Postcard image
Decide on how the piece should be exhibited