Don't take the above comment as a negative (OP) because I want my boss to buy this yesterday. We really don't want to manage servers or manage anything so SaaS and a good privacy policy/our security team not complaining is all that matters.
Edit: Just had time to go through the site, SSO would be important for enterprise.
In this case, the vendor probably needs to be replaced. That's the easy fix. The higher TTL will help as it won't be querying them, but then making changes will be a pain in the future, until unless you pre-plan.
These are some things I am have though about for managing DNS. Any other recommendations would be great.
1) Separate Registrar from the source of the DNS records
2) Multiple NS records on the registrar
3) Multiple vendors for DNS records with Terraform sync
between the two vendors
4) Limit A records or point A Records to CNAMES
5) Low TTL times for NS records, risky if you are hacked though or make a bad change