Stokke Flexi Bath Plug

We recently started using the Stokke Flexi Bath and I felt that the rubber plug is difficult to put back in place once its taken out (especially with an active baby inside the tub).

What I can do now with this is quickly replace the rubber plug once the water level is sufficient and it will drain the water at a slower rate. We bathe our newborn over the kitchen sink and the hole in this piece seems to equalize with our fully open faucet so this allows us to continuously add/drain the water while bathing.