Gene,
    I'm not sure what you mean by :
"1. The spec sheet for the connectors call for a drill of 0.007in with a
finished size of 0.006in "

If your drill size is this small, therein lies your problem.
Most likely a typo though, so I will try to explain some of the
problems in my experience.

One of the specifications from ERNI or AMP  is:
.024 +/- .002" (.6 +/-.05 mm)  and one is
slightly larger (can't remember which right now).
They have identical spacing / pitch.

You need to specify .001 - .002 copper in hole.
and finally the assembly vendor needs to use the
correct equipment to install the press fit connectors.
(i.e. proper tooling to support the back of the PCB while pressing
the connector in, and you need to have supplied the correct clearance
on the back side to allow this)     There may be more variables,
but these are the ones that bite frequently.

Good luck,

Karl