Congrats to your DD for acceptance into the research project!
If you’re looking for other options on getting to EDI, it might be worth trying to fly into LHR, then either taking a BA flight to Edinburgh or heading into the city to take the LNER. Might give you more cost-effective options, plus you could always spend a few days in London on either end of the trip. AA flies direct to LHR from a few airports and usually has biz class award seats for 57.5K AA points (you’ll probably have to pay a few hundred in taxes, but it may be worth it). I’d recommend booking the legs as 2 x 1 way tickets because it’s much easier to make changes to your itinerary.
AA has daytime flights to LHR from ORD and JFK, which would make economy seats bearable for the long flight, then spend a night at the HGI (Ts 2 & 3) at Heathrow or the Sofitel (T5 where BA flies from), then take the first BA flight to EDI in the morning. Super easy, but it means positioning flights, which I don’t mind to save points / money, but it depends on you and your family. Also if anyone in your family has SWUs with AA you can book an economy fare and get a free upgrade to biz class at the time of booking (you have to make sure the flight has upgrades available, which the call center CSRs will help you with since AA removed the availability for customers to view online)!