Thank you all for the replies and contributions.

With respect to checking with the embassy about changing the validity of the visa, we're working on that, but reaching the embassy is proving to be difficult.

The TA (as mentioned before) is claiming he cannot make any changes at this point, after the trip has already commenced. I'm still somewhat skeptical of his "inability", but have not heard your experiences on TA's general change limitations.

After 6/7 long calls with AA in both the US and UK, and a visit to the BA LHR counter, it is very clear that there are indeed no viable alternatives (the most inexpensive are $3000+). In fact, I found a RJ LHR-JED flight on July 9 that costs $750 online and told AA hoping that they'd accommodate us there since RJ is part of their alliance, but AA (after a long hold of course) asked for $4,000 to make the change!

At this point, we're pondering just purchasing the RJ ticket online and cancelling the original segment. Do you guys foresee any issues with that in completing the trip? Might we have to pay to cancel or do we only pay if we decide to use it later? Of course, we'll ascertain the changeability of the visa dates first.