There will be very little change in taxes and surcharges, generally OW adjust total cost of EU-US and US-EU fares by varying the base fare with the surcharges more or less being the absolute floor.
This is why having some TA, even an OTA, is beneficial. I have found AA and BA to be horrible with understanding their own fare rules, especially things like this where the customer has some flexibility. They are used to working with fares that are not changeable at all and struggle to accurately apply the historical fares rule.

With enough work you can find a routing that works with the routing rules, the idea that there is no I space for 5 pax because it is high season is not accurate. I buy 5 pax in I class every year on similar routes, often not until February or March.

You can find I space, it’s just a matter of finding a competent AA agent to successfully price. You may need to work on seeing if they can reprice one pax initially to see if EF is not accurately reflecting inventory. You should also check this, I think you can change the O or D of you double open jaw and still access historical fares for other city combinations for your return, which may open more options.