Can't help on the dimensions, but congrats on your new purchase. We have the High Country 375 FL, it's a different floor plan, but that front living room (on all of them) are almost identical. You'll love it!
Just an FYI, we use short laundry baskets and they work fine on the rear compartment. Side compartments are used for folding chairs, poles, longer and bigger items. Pass through in the front under the living room, we store the larger folding chairs, tool boxes, and smaller tubs (like 9 inches wide and 13 inches long and 10-11 inches high for all the small stuff, and stack them. I found, going smaller is better, especially if the containers are clear. Small stuff is just much easier to store and find.
Good luck with your new camper! Just a suggestion? Don't buy anything until you actually get the camper in your possession. You will change your mind about where you want to store stuff. It took us about a year... really... to find a permanent settlement and a routine for where to stow stuff ... both inside and outside. We kept moving stuff until it found a truly logical place and had a truly logical flow.
2019 Montana High Country 375FL
2014 Chevy Silverado Duramax, 6.6L Dually