https://gravitywiz.com/documentation/gravity-forms-limit-submissions/
Gravity Perks is a great addon to gravity forms that does a lot of cool things. This particular add on would solve this problem – plus they have great support.
I found this on github – I gave it a try and it didn’t break my site:
https://github.com/uamv/gravityforms-custom-entry-limit
Not sure if that means per user though – but maybe worth giving a try. Not really clear by the documentation. The first perks will definitely solve this problem though.