The $35/day assumes 3 meals. When I tour, I usually eat more than 3 meals or, if I only eat 3 meals, I have a fair amount of snacks. It will also depend on what kind of food you like to eat. I like to eat dried apricots as a snack. While raisins are cheaper, I prefer apricots. On the other hand, my go-to "energy" bar is a Snickers, which aren't all that cheap either.

I don't have budgets for my bike touring costs, so I have never tried to figure out how much I spend for food. But, I wouldn't want to have to decide between eating enough food and spending more money than I had. I wouldn't combine food and lodging into a single budget. Otherwise, a turn of bad luck (storm, bike problem, wrong turn, etc) could force you to blow your entire budget on a pricey hotel. I'd recommend doing a test run of at least two overnights doing 50 miles days and seeing how much you eat and if you think you can continue that style of eating for 12 days. That would be a better gauge than how someone who isn't "big boned" might fare.

As for the cost of camping, with a bit of research, you should be able to determine fairly precisely what it will cost to camp along the way. You may also locate places where there are no campgrounds, which will help you find a less expensive sleeping option.