Please tell me the basic angles I should have my farrier stay within on my
horse who is a Quarter X that I ride huntseat/training level dressage.
I know that everything traditionally relates to the angles of the shoulder
and pastern.  Some farriers realize this, some don't, some feel it has more
to do with the shape of the hoof.  Could you clarify for me?

Most modern veterinary and farrier texts state that aligned, normal phalangeal
angulation in light horses is usually 50º to 60º in fronts and 45º to 55º in hinds.
QH tend to be on the high side of normal.  Assuming angulation somewhere in
the normal range, in terms of efficient movement, it's important to have the
effective length and angulation of pairs - fronts or hinds - to be as nearly equal
as possible.

I am moving away from the town that my current farrier is in and I need a new
farrier. I don't want to insult anyone's intelligence but I want to be able to say
"his feet need to be somewhere around [n] degrees for our riding style"

Style has nothing to do with efficiency.  If you nail a horse's foot to the ground in
the name of "style", sooner or later, the horse pays the piper.

It seems that around here the majority of farriers in this area insist on cutting all
the heel off and leaving toes a little too long in my book.  Maybe I'm the one who's
the moron but that style can't be conducive to a healthy foot/leg either?

If efficiency is measured in caloric expenditure in getting from here to there,
then a long toe and low heel are the antithesis of efficiency.  All else being equal,
efficient movement is the result of short levers and phalangeal angulation as
upright possible within normal parameters.