as the "owner" of the line and insist that without independant verification, your long distance carrier cannot be changed.
How it works
New company requests a port to their service to local telco, a request is made to the NPAC (a national manager of who getsa to bill againsts which number) who notifies old LD carrier that a change is being requested.
The old carrier may agree to the change and send a confirmation
the old carrier may dispute the change
in any case some time goes by that calls are made over the new company's lines which incur charges.
this takes a while.

To avoid slamming, the FCC can ask for independant verification.
If you insist that the local company demand independant verification, they will note the account. When a slammer tries to get your number switched, a company independent of the phone company will call and verify that the owner of the account approve the change,
that should solve any issues.
thanx,
bill