You may more readily find skirt at a Mexican meat market/store - if you have them in your area.
I would not go over a minute on the sear. You should not be able to even get your hand over the hot coals (around 1000 -1200 F)
The foil wrap being tight is a must.
Be sure to cut against the grain (perpendicular) as well. The bias cut is just cosmetic.
If you can find it ask for the onglet (hanger) cut and try this cooking method or a cast iron grill sear.
