Base fares:

AONE4 Ex-RUH: USD 9089
AONE4 Ex-KRT: USD 7584

Taxes and fees will be entirely dependent on the routing and choice of carriers. Since RJ is the only OW carrier serving KRT, if you use the online booking tool the ticket would be issued by American Airlines, which does so on behalf of RJ for online bookings. Having the ticket issued on BA stock would mean BA does the issuing, which would also mean that you'd be charged BA-imposed fuel surcharges for the entire itinerary.

As a rough rule of thumb, on itineraries I've recently priced using RJ for the first segment (e.g. ex-AMM, for example AMM-ORD-XXX) fees and taxes for a DONE3 have totaled around 10% of the base fare, i.e. around $600 on a ticket costing $6200.

For similar itineraries originating in TLV (same base price) but where BA was the first segment, and therefore the issuer (e.g. TLV-LHR-XXX) the taxes and fees have been more than twice that, right around 20% of the base fare. Of course stopovers in high-tax locations, like LHR, will only add to the total.

So I would say that asking for an ex-KRT trip on BA ticket stock will go a long way to reducing the cost advantage created by KRT in the first place.