Thanks all for the follow up messages. Ultimately I wound up just returning to CAI because it fit better with my schedule and managed to pick up a decent J fare back to the US from there.

The anecdotal evidence (QR-issued BPs seen) as well as the GDS affirmation that itineraries involving TLV and QR-stock will auto price are helpful. I was able to confirm with QR no issue with TLV being on QR-issued tickets.

As an aside, I have long considered myself quite knowledgeable on ticketing, routing and fare rules... dealing with a now-defunct ex-CAI RTW and trying to make various changes across airlines and routings have significantly added to my knowledge base. I've had to go up against some less-than-helpful/incorrect airline agents (and these are the agents manning the trade support lines, not general public).