... what would you expect to see at the output from the PA in tx mode with no mic input?...
The carrier is reduced by two steps.
First, balancing the modulator. Some designs have adjustments
for this, others don't. If the carrier is too strong then you may
need to modify the circuit to adjust careful nulling out of the
carrier. Other factors, such as construction methods and stray
capacitance, may also be a factor.
Second, the crystal filter. The carrier should be a little ways down
the slope of the crystal filter, so it provides perhaps 6 - 10 dB of
additional attenuation (depending on how steep the skirts are).
If your filter is too wide, or the carrier is not properly adjusted
with respect to the filter bandwidth, then the carrier may be
stronger. But first balance the modulator.
This all assumes that the driver circuits aren't oscillating all
on their own, of course.