BP is the only 16710 you can get, unless you can find an old Noob or LF. The BP is available with either a 3804B(2813 GMT) or Hangzhou 6460(2836 GMT). A VR3185 movement will fit, if you ever plan on modifying for a clone movement. The case isn't very accurate though, and you'll definitely want to swap the caseback for a thinner one. They come with a thick 16600 caseback.
Just ask any TD for a BP 16710 and they'll get it for you. You'll have to wait until the factories open up when the raids stop.