Ok, I was able to get my sun visor apart. It is a bit tricky to remove from the head liner - you need to use a screwdriver to press in the tab in the slot in the base. Then you need to rotate the tab counter-clockwise (looking up at the base), so it can rotate out of the headliner. Pulling the sun visor away from the windshield at the same time helps.
Our sun visors split apart down the middle. The two halves wrap around the rod. If you remove the 2 screws holding the sun visor together, you can split the visor, starting at the point closest to the mount. The two screws are behind the vanity mirror lights on either side of the sun visor mirror. No cutting of the fabric is needed to access the inside of the visor. Be careful pulling the 2 halves of the visor apart as they are glued together and the fabric is held on the visor by sharp plastic needles.
The sagging mirror is caused by a spring metal clamp being broken or unclamped. This clamp presses on the sun visor rod. The clamp is held into the body by 2 retaining tabs that must be bent back before the clamp can be removed. On my sun visor, the clamp had been unlatched. I was able to relatch it by using a screwdriver to press the two halves together. However, when I tried rotating the sun visor down, the clamp popped open again. When I tried bending the latch so that it would hold better, the latching tab broke off. So I ordered a new sun visor ~$80 including shipping.
It looks like the clamp should be latched together and the two sides click together. However, when this is done, the sun visor appears to be very hard to rotate, much harder than it was originally and the clamp pops apart very easily. Maybe some other part broke off.
Hopefully someone can use this information to fix their sun visor. If you can some how get the clamp to hold together (screws?), this would apply more pressure to the rod, but the clamp fits in a very tight space and there is little room for screws. The clamp appears to be made of very brittle steel.
I'll try to add pictures later.