Thanks for all the input. So far I've booked:

* Rome: Fendi Suites (Palazzo Suite 1)
* Venice: Gritti Palace (Landmark)

Still mulling over the implications of location in Florence.

I might change those around as prices evolve / I learn more, though.

I find it really hard to justify the massive price premium of Aman over Gritti when Gritti is so well regarded and the rooms in Aman are kinda austere and there's lots of reports of poor internal soundproofing. Good bathrooms and common areas though.