Here's a way to save time.
Use Ilford Rapid Fixer at 1:4 dilution. Fiber print fixes completely in 1 minute! My usual routine is, 1 min in fix#1, another min in fix#2, HCA for 4 minutes and into a washer outside for 30 minutes. Sometimes I pool paper in HCA if I am printing two. (but no more than 2 at a time)
I see a couple of problems with your current routine. Prints are pulling in fixer contaminated water for a while. As someone said, longer in contact with fixer, harder it is to wash it out. Also a bunch goes into fixer 2 at the same time. Do you shuffle? How do you prevent damage with that much handling?