1. It is not at all a fact that No Claim Divorce petition is disposed of faster,
2. The duration of case depends on the load on the court and also how the opposite party is contesting the same,
3. Normally police complaint u/s498A, DV case, maintenance application etc are filed, inter alia, to put pressure on the husband to agree for MCD,
4. You should file those cases to presurise your husband to agree for MCD,
5. You can sell your share of the joint property after pre-empting i.e. after offering it to be sold to your husband at the same price offered by the third party.