Welcome to FT Ardaghman,

My suggestion is as follows:-

If you HAVE to fly EI and are going to take these flights anyway, maybe you can check-in online and then when you go to the airport, have a friend / colleague hold your backpack while you bring any other luggage to fast bag drop. You could then take the backpack through security, having not shown it to check-in staff.

IME, the gate staff are not as strict as the check-in ones, and if the bag looks the proper size, you should be OK to bring it on-board ...

A bit of a risky strategy I know, but might be the only option for you?

Alternatively change your flights to an American carrier from SNN, and connect thru NYC ...

Good luck!