Replacing steel with bronze is a good idea. OT did not begin using their diamond head bolts until the early 1920's. I would simply replace the bolts where the holes are sound. For the damaged yoke holes, I would drill out, fill with a plug or dowel, and drill a new hole. If you remain concerned about strength, you might glue a hardwood dutchman (ash or oak or . . .) the width of the rail onto the bottom of the rail before redrilling the hole, maybe 1/8" or 3/16" thick and a few inches long. Stained and with beveled edges, such a reinforcement would barely be noticeable. Of course, since there are cap rails, new wood scarfed into place, with a new hole drilled, would not be much of a cosmetic issue, though would be a bit more work.
I don't know about flat-head carriage bolts, but standard-shaped ones are available pretty readily. Maybe filing the head of a regular carriage bolt flat would do the trick. As I recall, OT's bolts are 8-32 diameter, and replacements may be hard to get that size. 10-24 is only a bit larger, and is more readily available. 1/4-20 is pretty readily available, but I would not want to enlarge a gunwale hole to that size if I could avoid doing so.
Stainless steel would probably work also, and is more readily available than bronze.
I have dealt with the Bolt Depot and received good service and good prices; they have stainless steel in the 10-24 size, and bronze in 1/4-20, which requires a larger hole, of course.
www.boltdepot.com
I’ve heard good things about Top Notch Fasteners. They carry fin neck flat head bronze bolts, but only 1/4-20 and up, and also bronze carriage bolts.
http://www.tnfasteners.com/index.html
Many woodworking supply places sell connecting bolts for knock-down furniture that have very flat heads and would appear to be ideal, except that they are steel -- though many are finished in a bronze color, I doubt that such a finish adds any corrosion resistance.
Greg