I'm of the camp that no raingear is really breathable, certainly not in the context of an aerobic activity like cycling. The capes are interesting possibilities. I've used a poncho walking/hiking, but never tried one on a bike. More venting than a jacket, but a bit more awkward. If you look at cycling jackets, look for armpit vents, chest/pocket vents and a vented (or mesh) back.
I'd suggest a partial change in really wet stuff. Wear your shirt, but bring the pants and workshoes in a bag and wear shorts. You can wear a jacket (or cape) and not have to worry about the waterproof bottoms, and changing is a 5-minute task of pulling on pants and shoes.
Or, ride slowly in full rainsuit and enjoy the rain.