As Kiwi Flyer mentioned, the transit process at RUH is not the easiest, or at least it wasn't for me. My situation was a bit different as I was actually arriving without a visa (not just transiting; it's a long story) but I had the clear impression that even a quick transit would be confusing to ground staff and immigration officials, perhaps because so few people do it there.

Of course, YMMV and everything may be very smooth in your case. Looks like a fun itinerary and trip!