The easiest way to procure a rabbi who will facilitate the Get and not try to change your mind is to already have completed a civil divorce, custody and alimony arrangements (if need be) and no no longer be living under the same roof.
Rabbis generally accept those circumstances as a fait accompli. As a family law attorney who has handled divorces for many decades I am speaking form my clients’ experiences. I and a number of Jewish divorce attorneys keep a file of Rabbis who can move things along.
Locally, I use a Chabad rabbi (multi generation family in the community). He has one quick phone call with both divorcing parties, arranges a convenient date and brings in a scribe from NY and supplies the eidim from his school staff.
From start to finish can be as quick as ten days,
Some clients don’t deal with a Rabbi, instead they call a Beis Din directly.
Unlike years ago, now one must make sure the Get is issued by an authority recognized by the Rabbanut in Israel if there is a chance of either remarriage there or additional children that may be born who might want to marry in Israel in the future.