Your understanding that there is no ineligible downfield penalty is incorrect.
For your purposes, all of your backs and the ends on the line of scrimmage are eligible. There is no foul in NFHS for having an ineligible player uncovered.
Since your league does not use the numbering rules, are they requiring any kind of special identification for the eligible players?
That formation is legal to run or pass out of. The Y player just cannot go down field on a pass play where the pass crosses the line of scrimmage.