Hi from another Minnesotan, Jason.
Do you feel the trip doesn't seem to congested, or burdened with
traveling?
Arg, sorry but I think you're trying to cram way too much into way too little. As previously pointed out, one of your two days in Rome is likely arrival day so it's only a partial, and a jet-lagged one at that. Whatever time you have on that day won't be much good for more than a walkabout to try and stay awake until bedtime ROME time. That leaves you only one full day in the city: you'll barely get your head around it with that little bit of time.
You'll lose 1/2 day or so with your other two moves plus you " would like to visit Pienza, Siena, and Montecello (Monticello Amiata?) while in Val d'Orcia." That's a lot of day tripping, and very little time at a "luxury agriturismo" you're asking about. As noted on that other thread, you would need to rent a car for your stay in Val d'Orcia, and do you homework regarding the ins and outs of driving in Italy: specifically, where you are and are not allowed to drive a rental. People do it, of course, but, well, do the homework.
With just 7.5 days to work with (I'm subtracting that partial day from Rome), I don't think I'd choose more than two bases. For a first-timer, I'd say add time to Rome and spend the rest of it in Florence, taking day trips to Siena (bus) and Lucca (train) as a substitute for Pienza/Monticello.
I know, not what you wanted to hear but IMHO, it sure would make things easier and less rushed.