We face a similar situation and we sometimes introduce API changes that break the monitors, which then requires to manually fix the testing script. The pain hasn’t been big enough yet to make us search for a different solution. Note that we are using Monitors mostly for end to end, user like tests, which represents a small fraction when compared to our unit test suite covering the API (where tests tend to be quite E2E as well).
We do use the one way Postman -> Github integration though. Every time a change is done, it is committed to a dedicated Github repo. We use it as a backup in case anybody messes up the scripts
We introduced two-way sync with GitHub, GitLab, BitBucket etc recently so you can keep your Postman collections inside version control while being able to work with them inside Workspaces. Details here: https://blog.postman.com/the-reimagined-api-first-workflow-f...
Plus, if the API moves, we had to (manually) find and fix dozens of Postman tests.
I'd appreciate it, if you have some insights that can move my team forward.