You are supposed to be seated within 15 minutes of your ADR time. You are requested to arrive at the restaurant 10-15 minutes before the time. For instance, if you have a 6:00 ADR, you are requested to arrive by 5:50. You are supposed to be seated no later than 6:15.
Just a thought--the onset of action of insulin is about 45 minutes after injection with the peak effect being 4-8 hours after injection depending on the type of insulin used. Would it work for you to arrive at the podium 15 minutes early (as requested), and ask the CM about how long you can expect to wait? If seating was basically on time (by 15 minutes after ADRs), DH could excuse himself to the restroom and inject the insulin. It is usually only a few minutes after being seated until the server approaches, and 5 minutes later you have given your order...5 minutes later your appetizer arrives. Thus, you should have your first food no later than 15 minutes after being seated.
I realize the need for refrigeration--I carry an insulated bag as a purse at WDW. Could something like this be used for a single dose? How about the bags made with cold packs designed to carry pumped breast milk (these used to be given out free in OB units at hospitals...)
You can never guarantee when you will be seated, but a simple word to the CM at the podium should get you in as needed.
