Hertz has pretty much the restrictions you list: MB and BMW models, convertibles, SUVs, Fun Collection and Prestige Collections vehicles not allowed into Italy.
Sixt and Avis: Exclusions vary wildly. Best to do a (dummy) booking and study the fine print during the process or book over the phone, following up with email verification. Had a clubsport GTI recently that had a lot more restrictions than the usual VWs.
Europcar: does not allow full size and higher cars into Italy. This basically excludes the three premium brands (Audi/BMW/MB) from A4/3-series/C-class on upwards. But I had no problems with a Passat wagon, which is classified "Intermediate" but way bigger than any 3-series or C-class which are classified "full size". Those mostly come as TDIs, are nicely equipped and frugal while torque-rich. You'll be able to putter along doing 220 on the autobahn
Europcar also has an interesting and definitely fun-to-drive selection of vehicles in their "compact Elite" group (Audi S3, Golf R - even as wagons!) which might be OK as well. Call!