When I do double sided boards, I plan ahead knowing there are no plate through holes.
If a component needs to be connected to a ground plane but covers up it's solder point,
I place a trace on the solderable side that is as short and thick as possible that leads
to a point where I can make a "via" to the ground plane. If there is enough clearance
under the component (or you don't mind it sticking up a bit), this point could be under
the component. You could also make the hole for the component a little bigger and just
solder an extra wire through the hole before hand to make a plate through hole.