The closest match that comes to mind would let your players bank the time they don’t use. Using an n+5 configuration. The software cutechess may be capable of it but it’s not online.

But what bugs me is it would be a goofy way to play as different positions can demand more thought than others.

You would probably need to make your own custom rule set and host it yourself or do a regular game on something like lichess and enforce the time constraints outside of the platform.