I haven't found a good tool to help with or automate any of this and I'm thinking about building one.
Do you care about this problem? How do you solve it? What's it worth to you?
It's all just a guess anyway. You can't make it exact unless you're psychic and know that next quarter will be a big one or a bad one.
But from my experience as a self-employed (in the US), you are in “safe harbor” if you just plan to pay at least 90% of last year’s tax bill (spread throughout the year) and then estimate any additional taxes due in January prior to the April deadline based on end of year totals.
Again, it’s just a suggestion, so discuss this with your tax accountant.