Mesa 7i96s and 750W AC servo

Just as I suspected.

There's no such thing as "sorta" NEMA34.  Your BLDC is a standard 80mm servo frame.  The bolt pattern is very close, but not exactly the same as NEMA34.

This is good news, actually.  Your mounting plate will accept an 80mm servo with no modifications (i.e. no die grinder, file, or fiddling).  Had you bought that NEMA34 86M-DHT (DMM) servo you'd have found that the bolts didn't line up, and the shaft wouldn't work because it's 1/2" (12.7mm).

The 86N-DHT is the metric version of that motor, and has an 80mm boss, the correct bolt pattern, and a 14mm shaft.  Drive is ~$270, motor is ~$300.  Plus cables, so ~$600-$700 for everything.

However... there are more powerful 80mm servo motors available at much lower cost than the DMM.  Specifically, the StepperOnline T6 series 1kw servo & drive kit.  These are rebranded Leadshine servos, BTW.

Servo drive & motor kit is only ~$270, shipped from the US.  3kRPM rated, 5kRPM max.  30% more torque than the DMM 750w servos.  Very easy connections, although it can't use 0-10v analog in signals.  You will have to run the servo in step & direction mode, but LCNC works well with S&D spindles.  Has decent encoder output signals from the drive (with index), so if you use a 1:1 pulley ratio you can do rigid tapping with no additional encoder needed.

The only downside (for you) is that the motor shaft is 19mm.

This is easily dealt with, however, by replacing the motor pulley with a different one.  I'd recommend using a taper-lock or QD pulley and purchasing the appropriate 19mm taper-lock or QD bushing.  These mounts provide a very firm grip and very concentric mounting.  Check out the B&B Manufacturing website; they have excellent online support for finding the right pulley/belt/bushing combos.

Your mill probably has an HTD-5M belt, likely 15 or 20mm wide, and what appears to be a 50T pulley from internet pics.  Just count the teeth, measure the width between the flanges (should be about 1mm wider than the standard belt size).

If you are willing to fabricate a different mounting plate/assembly then we can explore other motor options.  But I suspect you just want your mill working ASAP and this is the quickest/easiest thing I can think of.  It's not ideal, and I'm concerned that the motor will run very hot when buried inside the head, but this should get you going pretty quickly for not much money.

While you're thinking about it, have a look inside the head and see if you can figure out a way to get a 24vdc fan inside and some vents to cool the motor down.