I would look for a roomier enclosure than just a bivy sack or small net tent for a long-distance cycling trip. I don't think you can cycle 12-13 hours a day like thru-hikers walk, so you'll be spending bit more time resting in your shelter. Bugs will be an issue at many points along your route. Something like an MSR Hubba or Tarptent Rainbow would probably be nice. An issue to resolve is how, if at all, you will protect your bike from precipitation. You could just drape a poncho over it or something.
A true 40 degree bag or quilt would probably be sufficient for you. Lower temperatures are unlikely unless you're up in the Northeast in early September. For much of your route you will probably have much warmer nighttime temps in the 55-60 range. Regarding Synth or down — I don't think it matters a ton.
On a bike, compactness probably trumps low weight as a consideration for a lot of gear. Therefore, I'd take an inflatable air mattress such as the Neoair, mentioned above. I personally use the BPL Torsolite, but I'm sure most people would agree that the Neoair is more comfortable.
Since you'll be on wheels, you'll have ready access to HEET in gas stations. I personally would go with an alcohol stove, such as the Caldera Cone mentioned above. However, you'll build up an appetite within a week or so, and 550 mL probably won't be enough volume for the big meals you'll want to have. I'd go with 850 to 1000 mL.
For raingear, you'll probably want a full waterproof-breathable rainsuit. I haven't tried biking in a poncho yet but intend to try soon. Since you won't be riding through brush, consider the flimsy Frogg Toggs or O2 Rainsuit. No need to get goretex or eVent, IMO.
Some eVent rain mitts (e.g. from Mountain Laurel Designs) would be useful to protect your hands from cold rain, and you might consider Rocky goretex socks. However, most of the time the rain will probably be warm, and putting on all this raingear might make you overheat. In that case you'd just want some good quick-drying clothes.
You could probably find most of the items you'd need on the Gear Swap forum.
That'll be an exciting trip. I hope to do something similar some day.