Alternative would be to have it absorb quanta to function...
That way you could indeed still spam frogs, but you would need a decent chunk of off element quanta to do so.
Considering that this frog has a high price already that should be enough to mitigate potential for abuse with mitosis.
It would also be a good way to work in a synnergy with a second element. I think
would be a good choice since multi-ability use effect has already been established by SoR, so it helps to keep that little niche for time's theme intact.
Maybe something like:
"Startle: Absorb
per card in play to ready each card's skills.
Opponent may use skills twice next turn."
Or you can just assume that people know it will only be 1 time per turn since that is how SoR behaves.
There is no explicit statement that its bonus skill use effect cannot be used more than once per creature, but that is how it functions.