Zzzap

Dublin (DUB) to London (LHR) — Sat, Oct 28
American 6765 Dep: 7:30 am Arr: 9:10 am
1h 40m
Airbus A320, Business (D), OPERATED BY BRITISH AIRWAYS

London (LHR) to New York (JFK) — Sat, Oct 28
American 6214 Dep: 11:20 am Arr: 2:05 pm
7h 45m
Boeing 747, Business (I), OPERATED BY BRITISH AIRWAYS

New York (JFK) to Charlotte (CLT) — Sat, Oct 28
American 1808, Dep: 5:13 pm, Arr: 7:10 pm
1h 57m
Airbus A320, First (J)

Charlotte (CLT) to Chicago (ORD) — Sat, Oct 28
American 1866, Dep: 7:50 pm, Arr: 8:50 pm
2h 0m
Airbus A321, First (J)


Chicago (ORD) to Boston (BOS) — Fri, Nov 3
American 1119, Dep: 1:25 pm, Arr: 4:51 pm
2h 26m
Boeing 737, First (J)

Boston (BOS) to New York (JFK) — Fri, Nov 3
American 2314, Dep: 5:40 pm, Arr: 7:03 pm
1h 23m
Airbus A321 (Sharklets), First (J)

New York (JFK) to London (LHR) — Fri, Nov 3
American 106, Dep: 8:45 pm, Arr: 7:50 am (Sat Nov 4)
7h 5m
Boeing 777, Business (I)

London (LHR) to Stockholm (ARN) — Sat, Nov 4
American 6529, Dep: 10:45 am, Arr: 2:20 pm
2h 35m
Airbus A320, Business (D), OPERATED BY BRITISH AIRWAYS

Total cost for 1 passenger
£1,859.32

520 TPs so £3.58 per TP which round these parts is considered expensive.
But I don't think you'll necessarily squeeze much more out on a single PNR with ORD as the destination.
I assumed you meant Thursday 2nd November, rather than Tuesday.

How to book? You should be able to get this in to AA's multicity tool. If not, give them a call. Alternatively get familiar with ITAMatrix + BookWithMatrix.
The latter might be a good idea anyway as there are a number of minor variations on the above that you might prefer. I'm happy doing a 40 min transfer at Charlotte, you might not be...
Also, other US east coast entry points are possible: PHL, BOS, EWR etc.