Sunday, Memorial Day weekend is just about perfect imo, at least to close for any tweaking imo.
Catch a good local short track event on Saturday night, attend one of the two big events live on Sunday.
I did that one year and watched Fittapaldi win over Unser Jr on the TV, while grilling at the parking lot for the 600.
Or if you can't make it to one of the two races in person on Sunday, do the triple on TV.
Monaco, the 500, then the 600.
Lots of interim time between races, for eating with just family, or making a racing, grilling event with freinds.
Or just hunker down by you self for great day of racing and cheetos on the couch, and chasing the wife etc around the house between races.
As for the drivers, the big names can do the double if they want it bad enough. And doing both is still unique enough to add a little more glam or prestige if they do.
All things considered, the whole set up is almost perfect, with many options for a planning out a great day.