Wow, a dinner for 24 - I can see why you want to do some prepping ahead! Your beet salad sounds lovely.
You should be fine cooking the beets Wednesday for a party on Friday. I would peel and quarter the beets, drizzle with a little olive oil, and roast at 400F for about an hour or until you can insert a knife easily. Test after 30-45 minutes, depending how big the beets are. When they're done, cover tightly, refrigerate, and slice them the morning of your dinner.
I don't think I would shock them in ice water after cooking though, you'll lose some flavor as you'd see by the water turning red.
This is just the way I'd do it - hopefully others will chime in with more ideas.