Can husband stop equalization money if ex spouse remarries?

Based on this limited information, if equalization is the equitable split of assets, then that will still be done. Cohabitation or marriage does not change the split of assets.

Nope. This deal is now a judgment. The possibility of remarriage was known. No do overs.

The mediation is confidential so you can use anything that happened in mediation. Even if could, you can't go outside the four corners of the contract to explain it. If it is termed "equalization" then it is not spousal support. As you say it was waived. Why it was waived does not matter. Sorry.

An equalization payment can't be stopped by remarriage of the spouse.