My suggestion is to use epoxy resin as an adhesive. The epoxy is usually sold as 2 components in 2 containers (one is the epoxy pre-polymer & the other is a hardener which is mostly a diamine). Some of the 2 materials are placed on a piece of glass & mixed with a glass rod. The mixture is applied by the rod to the 2 rubbers that are to be stuck together at the points of joining.
This adhesive takes time to cure but it provides a tough and environmentally insensitive adhesion. Some experts claim that the epoxy can bond anything to anything (e.g.rubber to rubber, metal to plastic, plastic to wood...etc.). I used it to stick a plastic knob to a wooden cupboard & it worked very well.