One problem -- 700 x 28 tires is the max. Now I could get a modern "endurance" or "gravel" bike, but (a) I'm cheap and (b) it would be like abandoning an old friend. Sooo, how are the roads in general?
My memory is hazy since it was 11 years ago, but the only really poor surface I remember is a long stretch of road construction that I'd expect would be done long ago and even there we managed okay. I think my daughter probably was running 28mm tires even though on a bike that would accomodate much wider tires. Not sure if I was running 28mm or 32mm, but in either case i'd have considered them fine. Others may not have. Just as a frame of reference I started the Southern Tier on 23mm tires because I wanted to wear them out and put 25mm tires on halfway when they were showing cord. I actually enjoyed riding my old 1990 Cannondale Crit bike although the 23mm did buzz quite a bit on the Texas chipseal. I'd take that bike again with 25mm tires, but 28mm would probably be a smarter choice. I am probably an outlier in my willingness to run such skinny tires.
You mention carrying 13-15 pounds. A few pounds may or may not make a big difference. If you choose an entirely different bike or tire size because of how you pack it may be a pretty big deal, so I'll ask...
Is that including water and food? Carry what you want/need, but if you want to, that could certainly be trimmed especially if it doesn't include food and water. I have camped and cooked with a base under the lower number in that range and could camp and cook and include two full water bottles and a day of food and still be under that range if I wanted to or needed to. My current gear favorites the base gear totals is 8.5-9 pounds (add almost a pound if taking a the Whisperlite or SVEA instead of the pop can stove).
I know that I could easily get down to 4-5 pounds of gear and bags for CC touring even for contitions where I might get below freezing overnight temps and need some clothing for fairly cold weather (that would include clothing as warm as what I carried on the SC and on a winter Southern Tier).
A lot of how acceptable those choices would be may have to do with what you do with your off bike time. I pretty much ride, eat, rest, sleep, or do outdoor activities like hike. I never feel the need to dress up and don't mind being in riding clothes most of the time. Slippng on a wind shirt or a tech tee and running shorts off bike is about as dressed up as I get. If it is cooler maybe tights and a kayaking sweater, possibly with an UL windshell over them.
If you want/need to dress up more my approach probably won't work.