<<Disclaimer: Verify this information before applying it to your situation.>>

I also have major troubles digesting fats.  I do not have Celiac,
but gluten intolerance.  I'm now taking chewable digestive enzymes,
brand name Vitaline, from Ashland, Oregon.  I don't know
if they're gluten-free, but the ingredients label says:

Ingredients:  sorbitol, dicalcium phosphate, glyceryl monostearate,
beet root, magnesium stearate, mint flavor, silicon dioxide.
DOES NOT CONTAIN animal products, yeast, wheat, corn, soya,
sugar, phenol, preservatives, or artificial color.

The actual product name is  "Digestive Enzymes."  My allergy
doctor stocks these and I buy them from him.  I don't
know if Vitaline is readily available in health food stores.
They're pretty tasty.

I also had a stomach acid test which resulted in my taking
betaine hydrochloride with pepsin after every meal, since my
stomach is currently producing very little digestive acids.
Nature's Life produces a version of this.  It contains Betaine
Hydrochloride and Pepsin.  DOES NOT CONTAIN yeast, milk
or other dairy products, corn, wheat, gluten, rye, soy, rice
starch, wax di-calcium phosphate, preservative, flavoring
or coloring.  This might be a tricky thing for Celiacs to take,
considering the digestive injury, but I have no information to offer.

Nancy