Hello MaineTraveler, and welcome to the forum!
A whole month sounds great and you are doing your trip in the right direction - south to north - and hopefully this will save you a few degrees as it warms up in the south earlier than the north. July will be warm and busy so especially if you are staying in a place for a while I would look for a place with air conditioning that is a retreat from the buzz of the big cities. You are really late to start making reservations for next month so I would work to get the big pieces in place ASAP.
Rome, Florence and Venice can all support a week if you want to spend your time that way which really only leaves you a week to plan for. Rural Tuscany is as beautiful as advertised but is one of those areas that requires renting a car to really see because of the nature of the small scattered towns and the beauty of the countryside.
Rome is crazy and amazing so I would book a week there and start planning. You will also be coming off an international flight so an extra day won't do wrong if you have a 'lost day' to jet lag and in country logistics. Train to Florence on the fast train.
One alternative is to take trips from Florence - Arezzo and Siena are easily accessible and there are other days trips if that interests you. You could even train and stay a couple of nights in Siena to get a feel for a larger Tuscan town. Arezzo offers a smaller old town with fewer areas of interest but also fewer tourists if you want a quieter pace. You could shorten your stay in Florence a day or two and add those days - and maybe a couple more - and stay in Siena for that taste of hilltown Tuscany. Assuming you can find a place for next month.
If you want to stay on the Rome to Venice line there are several interesting cities worth a couple of days without heading to the west coast or Lake Como which means going through Milan. Bologna is a large university town with a great foodie culture that is just getting on the tourist map for many Americans. It is a 30 minute fast train from Florence.
Verona a very arty, mostly pedestrian, cafe culture city that has medieval buildings and a few sights (like an intact Roman arena) and is a great jumping off point for many northern towns - Brescia, Padua, Vicenza - and has access to Lake Garda which is a viable alternative to Lake Como without heading so far west. Verona has easy train access to the southern edge of the lake - which makes it super touristy - so look at Malcesine as an alternative which has a mid-lake ferry like Varenna does on Lake Como. Upper lake Malcesine would require bus travel from Verona.
The walled city of Lucca and Pisa are also Tuscan alternatives if not the rolling hill Tuscany that people think of from the photos. Both are worth a day trip from Florence and Lucca is great place to get a feel for the best of small, kind of upscale Italian life in a town of about 10,000 (inside the walls).
Venice is a conundrum. I love Venice but it is a logistically challenging city and I think you would really need to be charmed by its magic to spend a week there. I would happily spend a week in Venice by you can see all the "sights" in a few days and unless you are entranced by just wandering the city like I am you may find a week a little long. I would recommend a 4 or 5 days in Venice and after that you'll know whether you'll want to come back as often as you can or you'll feel like you've seen it.
Hope that helps, if you're not already making reservations stop whatever you're doing and start right now.
Have a great trip,
=Tod