Yes, it is definitely there. I suspected SLS from the way you described its super foaming action. Why don't you try the Toms of Maine toothpaste that I referred to in my detailed post? That toothpaste has no fluoride, no sodium lauryl sulfate and it actually foams up pretty nicely when you are brushing. It also does not irritate my lips like Colgate or other "regular" toothpastes do.
One thing I want to point out to you is that the toothpaste you are using has calcium carbonate in it. It is essentially chalk. This is something that is added to certain toothpastes and it acts as an abrasive. Each toothpaste has their own RDA (radioactive dentin abrasion) rating. Some are made known to people (consumers) and others are not. Some aren't even tested. The index rating is between 30 & 200 with any toothpaste being at 200 will pretty much scrape the enamel of your teeth right off.
If it weren't for the SLS, I'd say that this toothpaste would be okay to use. But for someone suffering from EC? Avoid SLS toothpaste at all costs. Once you are cured of EC then you can slowly begin to reintroduce (if you so choose to) older products you used to use because the lips will have that healthy epithelium back. The epithelium lining is what gives the lips that glossy effect when they are wet. You can refer to it in the same way that you can refer to the earth's ozone layer. It is a layer of protection.