I’ve used (and wrote) https://mockaton.com for this. It has a browser extension, which downloads all API responses in your flow.

then you can run mockaton with those mocks. you’ll manually have to anonymize sensitive parts though.

also, you can compile your Frontend(s) and copy their assets, so yo can deploy a standalone demo server. see the last section of: https://mockaton.com/motivation

mocks don’t have to be fully static, it supports function mocks, which are http handlers.

for demoing, the dashboard has a feature for bulk selecting mocks by a comment tag.

Surely real product with fake data is the answer. Fake data doesn’t necessarily mean “silly” data e.g. names like Larry Llama or myfaketestwebsite.com. There’s no reason why your real product running on sandboxed data should hurt your credibility.