I ride in a pair of "baggies" without a pad and a pair of padded underwear so I don't have to wash the baggies often. I carry a spare pair of underwear and as you point out they can be ridden in on their own......they actually cover up more than most lycra cycling shorts. I hope you don't use the Andiamo padded briefs, I would not feel comfortable riding in just those and certainly not walking into a store in them. I save the convertible long pants for camp and walking around town, but the shorts part on them are good fro riding in too.
i use the non padded andiamos when i get to camp, or if i need to change things up a bit (usually just for the first few miles).
For padded shorts I roll on some 2XU tri shorts (pad is super thin) or my Ibex bibs or knickers. I have a pair of ex-officio hiking / trekking shorts that I wear over, or in camp. Or a pair of MUSA knickers.