Congrats on 2,000.
A 1968 Carlton may well have been built for 27". You really need to know. If you've got even a 700c wheel, stick it in there and see how your available breaks reach. Then measure.
I've recently gone thru a very similar process. I acquired a great '63 frame, built for 27" and fenders. I spent a lot of time exploring a 650B conversion. In the end, however, I've been convinced to go 700c with 35mm tires.
First, I found that even 700c wheels required long reach brakes. I've gone with the R559. But, skipping many other details, the final straw was Chris K, the owner of V-O, who looked at me and said, "Why would you do that? The handling will be much better with the 700c and you can run as wide a tire as you want."
Heck, I went to him for validation. I got common sense.
That said, I still look longingly at those Grand Bois 42mm tires... sigh.
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1959 Hilton Wrigley Connoisseur (my favorite!)
1963 Hetchins Mountain King
1971 Gitane Tour de France (original owner)
* 1971 Gitane Super Corsa (crashed)
* rebuilt as upright cruiser
1971 Gitane Super Corsa #2 (sweet replacement)
1980 Ritchey Road Touring (The Grail Bike)
1982 Tom Ritchey Everest
(replacing stolen 1981 TR Everest custom)
1982 Tom Ritchey McKinley (touring pickup truck)
1985 ALAN Record (Glued & Screwed. A gift.)