A quick thought on wool - if it rains more than one day, that wool will become wet (or at least damp) and pick up a lot of weight and will not dry fast unless you get a major weather change. Good modern synthetics are far lighter once you see that wet and dry/lose water weight far faster.
I sailed the North Atlantic wearing the then new Patagonia expedition weight Capeline thermal underwear 9 of the 12 days. Life at 50 degrees. 50 degrees north, 50 degree air and 50 degree water. Everything was wet all the time. Water dripped of all the metal and glass inside the boat. We pumped water out several times a day, (Boat didn't leak a drop. It all came in with us.) Every time a crew member came below he brought in/let in another gallon of water. (Sometimes a lot more if he times it poorly with waves.) I was comfortable in that thermal underwear that I never took off. It would be soaking wet after standing watch on deck (the water in 60 mph winds will find every crack in your foul weather gear). I'd go below. peel off my gear and clothes and go for my soggy sleeping bag still in the thermals. And sleep soundly. Good stuff.
Get good stuff. In the break between the two big storms, I took off those thermal and put on old polypropelene thermals I had kept dry and clean in a plastic bag. Dry, clean and nowhere near the quality or comfort of that wonderful Patagonia gear. In 24 hours I could not stand the polypropelene any more and put the soggy good stuff back on for the next 4 days. Granted, that was a lotmore demanding than 3 days on a bike. Still, I would hate to see you suffering a nightmare of a bike ride. May in northern Ohio is a crapshoot. (Never liver there but grew up oin Boston and spent 6 years in southen Michigan. Both quite similar weatherwise. And both a real crapshoot that time of year.
Ben