"but at only 13 and 11 the kids are not old enough or responsible enough to leave them to make their own way to the gate."
Each to their own but T5 is one of the easier and safer places to start their "airport training". I am believer of unaccompanied flying from 12. BA raised it to 14 last year. Obviously child specific, well prepared, mobile phone in hand, and "picker upper" at destination before child's airplane takes off.
In fact age 8-10, guide me to the gate. 10-11 meet me at the gate. UM flying from 8 also recommended (start with shorter routes). Then 12+ I'll meet you at the starbucks outside arrivals (with age adjustments as needed).
Specifically in your case. Tour t5a together for familiarity, get them something to eat, sit them down somewhere not far from the escalators. Call them every 30 min from the lounge.
Well done on flying them in Y. Builds character. You would never want them in the future to not enjoy the greatness of world travel because they can't travel premium and when they do travel premium they will enjoy it that much more.