Mitt is definitely a way to go.
I dropped my clay so many times and had to change it over. Bar that was enough for longer, was used in half of the time.
Got 5 clay bars at wicked price some time ago and cutting small part of it every time.
Another thing to consider would be, to keep the clay cloth or mitt clean.
I use the clay piece only once, on both sides.
That way you’ll reduce all contamination picked up from paint to be dragged on it again, when claying next time.
You normally would remould it and keep it damp but what about cloth and mitt?
Try to take a piece of clay slightly bigger next time and mould something like a botch in the middle of flat part so it fits between your fingers. That should provide better control.
I tried claying in slo-mo and failed anyway.
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