Well, I got an X-compact grip last week, delivered on Friday... so excited...
Until I figured out my stock 320 mags wont fit, AND NO ONE has the replacement bases, nor 15 round x-style mags.....What a bummer. So it went back in the stock grips and I am waiting on the email from one of four places that I "got on the list" when the base plates come in.......

Cut/file/grind the two "ears" off your baseplates. That will tide you over until the replacement baseplates are available.

What’s the preferred method? Completely remove the ears resulting it a flat base pad? Or thin the ears similar to the newer style base pads?

Even any standard new P320 compact mags should fit. Mine do.

I also received the x compact grip. All you have to do is dremmel or cut off the side wings on the mag base. Very simple and worked excellent.

There's no such thing as x-mags. New style mags will work (look for the square peg in the bottom, thin dog-ears on the sides. Or just remove the dog ears. Either way works, and removing the dog ears doesn't impact the strength or performance of the mag.

Sig does sell replacement baseplates, but they're more expensive than Glock mags.

As others said just cut the ears off. If you don't want to go that far you can grind them down to fit but they are not needed so I would just take them all the way off.

Good to know. Thanks for the input... now where did I put my Dremel?!?

Mags are available from sig. they just sent me two.

I just used a set of flush side cut pliers to snip the ears off. Then I used 220 grit sandpaper to sand the remaining spots flush with the rest of the area, and 400 and 600 grit sandpaper to make them smooth.