I had the same kind of question. I cancelled my hair dye appt last week and just had a cut, don't know if I will keep it up, but I suspect I'll wait for 12 weeks. I get the impression from the NHS advice that they don't really know...But it suggests some wait 12 weeks, and 3-4 dyes over 9 months would only subject you to low levels of the harmful chemicals.
You could also get highlights slightly away from the scalp maybe? I have dark hair with light roots it's a mess already!