As from my experience, the way to find a solution I think is a combination such as healthy diet, not to care about your lips (that's the hard thing), to leave them alone (another hard thing)and having positive/good mood.
The first time I had EC lasted for about 5 years and I had been under all these staff, doctors prescribing creams and chemicals (which did not help at all)and till now I still do not know how it dissappeared for about 15 years.
It appeared again for the last 4 years and I am still trying to find out how to get rid of this. I gave a last chance to a derm prescribing me 'protopic/tacrolimus' that didn't help, carried out a very strict diet (that worsened my situation) and I am now leaving my lips alone (as much as I can) and waiting. Till now my upper lip is having an improvement but unfortunately I quite use lipstic at my bottom lip in order to cover the problem (which I do not know if this is 'acceptable' when leaving lips alone).
Steam treatment sounds quite nice/promising but kust to advise you : when you have your lips in a wet do not put yourself into temptation to force crusts to come off, I think this is wrong.
Anyway I will try your treatment and I hope everything will be fine.