This is a great tip, thanks for posting. This trick seems to allow me to finally combine some airlines that would form an itinerary on ITA, but not price out at any other OTA It also allows to price mixed Economy/Business itineraries which can be useful.

However with the tests I have done everything has to be booked through priceline; and priceline does not seem to respect the fare class - everything will be booked in the cheapest fare bucket for the cabin. So maybe not so useful for the OP - though very useful for other cases!