Actually the trailer is by far the best option. I have a friend who road across the country and back toting a trailer which must have weighed a couple hundred pounds ... he brought everything to camp, cook, and play amplified music by the roadside to raise funds. he started the ride to raise funds for cancer research, and carried on just to carry on. I saw photos of his rig---big old sealable trash cans and bins on a trailer, so he never had to worry about rain.

I have never used a trailer, but if i had to go absolutely car-free again, I would get one. there is no safe way to haul 4x8 plywood on a bike, or more than a couple 8' 2x4s. And as for shopping ... I can carry 90 lbs of camping gear on my bike, and add a couple hundred pounds in the trailer ... I don't buy that much in three months.

And with a trailer, i don't even need to bring my panniers and take the trouble to pack and unpack. Just dump it all in back and roll on out of there.