What happens to the shrinking universe in the presence of the pressure of Hawking radiation?
In a shrinking, roughly 3-spherical universe with only a black hole, Hawking radiation should follow a geodesic line and return to the black hole, without excerting radiation pressure to the universe as a whole.

Therefore it's hard to see, how Hawking radiation should establish an equilibrium with gravity.

More feasible seems, that the shrinking universe can prevent the black hole from further evaporation at some point, since evaporated particles and radiation are directed back into the black hole by the overall curvature of spacetime.