Stephen, (2) was a response to your thought about abandoning CC. I was pointing out that if CC won't work here, there's no need to look for an alternative.
As for other suggestions, after having tried your About page and seen that CC is being disable there too, it seems that your slider isn't the only candidate for setting the constant.
You need to test on a staging or test site by disabling your plugins and seeing when CC starts to work. Then, if appropriate, see if you could use an alternative that does not set the constant.