5th gear popout/torque reaction noise: Motor mount?

[Dan Mitchell]

I have a 1991  ser which in the last 6-8 months has developed 2 problems I
think might be related.  1st, it began making a low freq rumble/growl when
backing up.  Seems worse in the cold, and only by slipping the clutch a lot
is it avoided.  Sounds kinda like it could be an exhaust leak, or maybe
exhaust noise being transmitted into the car as the exhaust contacts the
body somewhere.  It also makes the sound briefly when quickly going forward
over large dips in the road, again especially when cold. Looked at the
exhaust (stock, all new except cat about 3 years ago) no obvious leaks,
hangers  etc look ok. 2nd problem is 5th gear popout.  I've read this is a
problem with a bad  design on the 5th synchro, but I'm wondering (hoping)
that these 2 things might be related & may be caused by a bad motor mount.
I notice when I blip the throttle, the shifter does move a fair amount (top
of the knob moves maybe 1"-1.5") don't know if this is excessive or not.
I've had the car since new, it has about  110,000 miles on it.  I put in a
new clutch about 3 years ago (along with the exhaust parts & new Raxles
axles).  Comments?

Thanks,

Dan