I have a Delta Contractors, very little use on it . . . My saw, same as you I'm sure has "ACME" type threads on the arbor. You are in luck, I also have a new Freud 8" Dado Set that comes in the Red Carrying case. I just walked out to the shop and initially experienced the same problem.
I tripped over the solution.
1. make sure your arbor is as high as it will go, "better access"
2. hold the chippers, spacers, etc . . @ 9:00 & 3:00
3. approach from the side where you are facing the end of the arbor.
4. I found that in this position I was able to slip all pieces on easily.
5. yes, the shims dropped into the threads, but a little feathering on the bottom like drumming with your fingers while doing the same on the face of the shim that slid right on.
6. yes, the tolerances are really tight, but they will slide on
7. also make sure you don't have a burr on your arbor from a dropped blade from a prior changing, or a scar caused by the plates used normally to hold a single blade.