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. Increment ranges go from 0 to 180 seconds.

15 seconds plus 5 seconds per move should be doable.

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.