repairing my 68 grill

I think I know the slots you are talking about. There's two that attach to the center latch support that goes in front of the radiator, and then two that attach near each of the headlight bezels to the radiator frame. I got rid of my center section support if you need a different one - I had to take it out to put an intercooler in.

I don't think having the grill secured at those two points will help with the hood shake. That center section is tied in with 4 bolts on the radiator support frame, and the grill only attaches to it to keep the grill ridgid. I had an issue with my hood bouncing and found that the bump stop on the driver's side was bent downwards just slightly and not actually making contact with the hood. I eventually went to hood pins due to removing the center section, but I suggest looking at the bumpers as they have to push up on the hood while the latch acts downward to keep it from moving up and down.

As for the grill, I'm sure it can be fixed if you have the missing tabs, or a way to create some.