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.
AnAustralianPhotographer@lemmy.world 2 months ago
You could go to lichess.org and create your own time controls. They let you stipulate an initial time and an increment.
For example you could have a game with a 30 second time for each player and then add 15 seconds for each move after that.
I believe the time would be banked for each move rather than a hard fixed limit for each move.
You could then create a custom game open to others, or make the game available by link to a friend.