The "rinse" cycle is to stop the phosphating process, and to cool the parts for handling. I use a large wash tub with 8 to 10 gallons of water to lower contamination from the previously dipped parts. To dry them, replicate the warm, dry California sun. Try a heat lamp and a small fan on them, for 15 or 20 minutes to evaporate the remaining moisture, then oil. I sun dry on a towel. Compressed air has always left a rusty "flash" when I've tried it, and a warm oven is just as bad. Hot 20 or 30 weight stinks up anywhere it's used so I prefer WD-40. On moving parts like a hood hinge, I flush the joint with WD-40, catching it in a pan and back in a spray bottle for more flushing. Obviously when the joint runs clear, it's flushed. I haven't experimented with baking soda to neutralize the acid from the bath.
Have you considered using shower rings on small parts with a hole? From bead blasting to spraying with oil they stayed "ringed". How about "plumbers tape", the multi-hole steel strip? This is for bead blasting only, I use a stainless multi-hole scoop for handling in the blackening dip, and a second scoop from the phosphating tank. A fish poaching pan works on long items like center links.
Jim