Switching to mostly gi training helped my whole team by leaps and bounds. The gi forces you to slow down - at first because you can grab cloth to stop your opponent's explosive movements, but then later on you just get so used to being tight that when you take the gi off you instinctively go back to no-gi grips and STILL stay ultra tight with them (something that most nogi-only guys don't do), which is part of where the whole "gi makes your game more technical" comes from. The other part is that because you are grappling so much slower with the gi on, you get to experiment a lot more and develop many more techniques in your arsenal, and especially if you are coming from a no-gi background already they will NOT necessarily be dependent on gripping cloth. When I roll, I still use the same grips 90% of the time whether I've got the gi on or not - the only real difference is if I'm training for an upcoming gi competition I might grab the gi a bit more, and obviously collar chokes require gripping the gi. We now roll one day a week no-gi in my school and everyone's progress in no-gi has accelerated if anything. As someone who used to argue that you didn't need the gi to get good in no-gi, I have done an about face in my opinions. The gi - especially for those below purple belt - should be used at least 30-50% of training time, I feel.
As far as physical demands, rolling with the gi is a lot less cardio-intensive. Overall you'll get a lot less injuries, too, although your fingers will take a pounding. If you switch to mostly gi training, you WILL need to make sure you do some sprints or other anaerobic cardio to keep your endurance up for no-gi competitive grappling. A few hours a week of hard no-gi rolling will keep you in shape also.
I don't believe there is any "ideal structure" to a gi class, or a no-gi class for that matter, in terms of instruction, drilling, live rolling, etc. I think it is a very subjective thing that should CONSTANTLY be changing according to the class' needs, which any qualified instructor will automatically do anyway. Some classes will be an even mix of the three, while other classes will be just for drilling, or just for rolling, or just technical instruction. The "ideal structure" is what contributed to the dilution of the TMA styles effectiveness, in my opinion. BJJ needs to stay fluid, dynamic, and in a constant state of adaptation to the needs of the group and the individuals.
If you are going to train at more than one school, I feel it is important to discuss it with all school-owners and establish who you are representing when you compete (if you compete). If you never intend to compete, I don't think it matters quite as much. I definitely would suggest the "exclusiveness" of gi in one school and no-gi in another, however, if you want to represent both schools. That is actually the situation I am in. I train and compete under Roy Harris' Association for no-gi, and under the Joe Moreira/Aaron Blake Association for gi. I was up front with everyone about it BEFORE I made the switch to dual-affiliations, and after a few initial hiccups over the whole "who are you representing in competition" and "who are promotions going to come from" stuff, I think it has worked itself out well.
I know this has been a long post, but as someone who is in the situation that it sounds like you want to be in (dual-affiliations), I wanted to answer each of your questions. Please let me know if this helps, or if you have any other questions.