You’re going to have other problems than the brackets because shortcode_parse_atts will have already parsed your attributes, and the various single and double quotes will confuse the regular expression used to do that.
If you need the exact string, perhaps you could get it from a custom field. Alternatively, and better, you could specify a number of attributes for your shortcode (time1start, time1end, time1color, etc.) and rebuild your Javascript at the back end.