Difficult soldering problem

I am dealing with a rather thick printed circuit board (0.185") which
is populated mostly with surface-mount parts on one side. However,
there are also some SMA vertical RF coax connectors. We are having
difficulty getting the connector pins to solder well to the board,
which has ground planes on both outer surfaces. The heat treatment
appropriate for the surface-mount components does not work well on the
deep plated holes for the connector pins, and the solder does not flow
into the holes.

I have thought about injecting solder paste into the holes and heating
each connector separately. Any other suggestions?
.