Strip the paint. The strength of the contact cement depends on it's bond
between the two objects being glued and it's self. In a normal situation
this would be wood, glue, wood. By not stripping the paint you are making
the strength of the glue dependant on the bond between the paint and the
Your sandwich consists of wood, paint bonded to wood , glue bonded to paint,
glue to glue, paint bonded to wood again, then wood.
The bond between wood and paint isn't going to be all that strong.
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