Like so many things in Saudi, you just have to take a deep breath.

The advice above is good. Stand in the line next to the GCC line. Hold your passport open with the stamps all over the visa visible to the wandering enforcer who stops non-GCC people going into the GCC line. And hope. I also bought a green plastic Saudi passport cover for my passport from one of the hotel gift shops, it has only helped once though

The fingerprinting has been active at least a year, it has been chaos ever since... it's most annoying they can't link the old fingerprints to the new visa.

I tried to count the number of times I've done the Saudi immigration line, but stopped caring when I got above 100 (My current passport will soon get its nineth Saudi visa, durations between 1 and 6 months, and there were a couple in my previous one...)