Don't know much about HA formulas as I bfed, but I did go on a dairy elimination diet for my ds' eczema when he was younger! Eczema/asthma/allergies are all interconnected, so an allergy or intolerance could definitely be impacting his skin. Dylan's since been diagnosed with multiple food allergies, and since we've gotten all of that sorted (eliminating the foods from his diet and mine) his skin has improved dramatically!
I do know that HA formulas can be pretty foul tasting - if you find that he rejects the taste outright, you'll likely have better luck if you slowly make the transition by mixing it with his current formula, gradually increasing the concentration of the HA formula over a couple of weeks.
Good luck, and I hope that it helps!