Clinique do a Take The Day Off Cleansing Balm. I haven't tried it but it looks a quite mild formula (no essential oils etc.). I would be enclined to give that a try first over the EH one if your skin has been playing up.
I agree to that because the EH Balm has essential oils in it that could also cause a reaction but at the same time, in my option, yes, it is gentle and I have no problems with it (I have sensitive, dry skin). I am also using the Hot Cloth Cleanser from Boots' No 7, maybe this is also worth a test for you?