I cannot speak to the theory. But, if one starts out with the classical "bounce" intution, one then arrives at the escape velocity issue you and the OP are noting. I was trying to point out that the escape velocity argument may not be relevant, because of the assumption/intuition which went into framing the problem, as stated by the OP.
In general, yes, the escape velocity would need to be overcome. But because it would need to be a quantum and general relativistic phenomenon, there are quantum and curved spacetime effects which make framing the problem as simply "escape velocity", a potentially problematic approach.