Tony, I am also a Clydesdale and dambed proud of it. I realize that I am not going to be competitive; in fact, when I was interviewed about my cycling experiences for my hometown newspaper the reporter tactfully described me as “built for comfort, not speed”.
In these circumstances, I have opted to avoid narrow, high-pressure tires and have instead embraced the old-school standby. I’m still riding 27×1¼ tires (which, if you’re using 700C wheels, would equate out to something along the lines of a 700×32), and I take pains to keep them up to around 100 psi. The extra volume cushions the ride slightly more than even a 27×1-1/8, and keeping the pressure up to the max prevents pinch flats — and my experiences tell me that these are the causes of the vast majority of flats on a ride like RAGBRAI.
Not to say that you can’t or won’t pick up that odd piece of glass or sharp stone, or the thumbtacks that some local bonehead tosses out onto the road, but if you keep an eye open you can more than likely steer around these hazards; if they are completely unavoidable you could always make a quick stop to brush this debris from the tire before it has an opportunity to penetrate.
You might also want to check out the rim tape that is covering the spoke niррles and make sure it is in good condition. Not every flat is caused by something puncturing the tube from the tread side of the tire. And while you’re at it, run your fingers — CAREFULLY — along the inside of the tire itself. If you feel anything sharp, remove it before remounting the tire.
Of course, if you WANT to spend the extra money on Gatorskins or tire liners — and as far as that goes, didn’t Michelin or some company make a “steel belted” bike tire with a fine screen in the casing? — and if it makes you feel more comfortable, then by all means be my guest.