More speculation with regard to Jupiter's power production mechanism:
The gravitational binding energy of a spherical mass is ~ G*M^2/R, so
gravitational contraction would "release energy" (sorry Jim) at a
rate of
dU/dt ~ (G*M^2/R^2)*dR/dt
You inferred a net power out of 1x10^19 W which, given Jupiter's mass
of 2x10^27 kg and radius of 7x10^7 m, could be produced with a
contraction rate of
dR/dt ~ 2 Angstrom/s ~ 6x10^6 m/Gyr
This would almost certainly be undetectable, but it also seems
perhaps an order of magnitude larger than I might find reasonable.