If one has a normal bite but a profile with a weak chin, would pushing forward against the maxillary teeth with the mandibular teeth at rest help their case?
No, the forward movement of the mandible is made possible by a muscle attached to the sphenoid and the maxilla, so just like trying to lift your legs, it won't work. Instead just let the mandible get slightly pushed against the TMJ joint by mewing. IMO weak chin isn't caused by movement forward/backward, but by changes to gonial angle/ramus angle and angle of the teeth. Also actual mandibular growth also impacts recession. You can have a perfectly parallel bite and a very sharp gonial angle, yet not good projection because of lack of mandibular growth.
You should just keep mewing, your projection of the mandible will naturally improve from it.