Are you measuring your waters temp or the beer temp? If you just added the frozen water bottles, the beer temp shouldn't drop that fast (from how I understand things). There are smarter people than me here that know a lot more about thermal dynamics, but I think with the limited contact in surface area and the actual volume of liquid, the changes shouldn't be so drastic as to kill off your yeast, or even stress it out much.
You also say it was below 60F, but what was it before you added the frozen water bottles?
I use this method myself. My previous batch, I had used Nottingham, which I'd read in several places can put off off flavours starting around 70. It also has good tolerance for low temps, so I learned that switching out two frozen bottles every 12 hours can keep my beer at around 60. If I only switch out one bottle, instead of 2, it sits at around 66, which is what I normally aim for.
Once you've done a few batches using this method, you should be able to dial it in pretty good.
That said, my next step is going to be building a fermentation chamber. As much as I feel comfortable controlling my fermentation temps right now, I'd like to be able to dial it in more, and without having to constantly monitor it.