Is it permissible for a woman who is engaged to continue speaking formally with her fiancé after she has repented and vowed to God not to speak with him except after the marriage contract, if the fiancé refuses to expedite the contract?

The engagement is merely a promise of marriage; it does not permit the suitor anything from the fiancée except looking at her. The suitor is a stranger to the fiancée, so he should not speak to her or correspond with her unless there is a valid need and to the extent of that need. If there is no need, then it is not permissible for them to speak to each other. If you made a vow to Allah to stop speaking to the suitor with an intention, then nothing is binding upon you if you speak to him out of necessity. However, if the vow was made verbally, then an expiation for breaking an oath (kaffarat yamin) is incumbent upon you if you speak to him.