Seems we'll be spending a lot of time on the bus. I understand they will stow away the large luggage. but then they say will allow only 12"x11" x 6' (which is the size of a purse) carryon inside the bus. this seems completely inadequate for 20 day excursion! I think one should be able to have backpack that can accommodate sweater and umbrella at least.

If I ask Brendan, they will just refer to policy - my question here is how strict are the driver/handler if i bring backpack several inches larger?

The measurements you quote are the size of a tote or a small backpack. You can fit everything you need into that size including an umbrella or rain jacket. Do a search for bags with those dimensions. Any bigger an it becomes a nuisance on the bus and on excursions.

I'd just plan on obeying their carry-on rules. I could easily manage with what is essentially a 1' X 1' X ½' bag. That is about the size of my personal item when flying long haul. Everything I need for an overnight flight and the first few hours at my first destination fits (with room to spare really) Plenty of space for a folding umbrella, a cardigan or windbreaker, water bottle, etc etc