Here is another Snell, that is currently for sale. It interests me that the seller says the bike originally had 30" wheels! My frame and forks are relatively tight around my 700x38C tires. Slightly larger 28 x 1 1/2" TOC tires would certainly fit, but I can't see 30". I wonder if these bicycles were possibly offered in both 28" and 30" variants.
I'm interested to know if Darj's Dunlop tires are true Dunlop-type wired-on ("clincher") tires, and not single-tubes. I have a pair of TOC Dunlop-style wood rims, but I can't find any current size tire that fits them. Is there a size marked on your tires???
A last question for Darj is if your stem bolt holds your stem to the fork, or just the handlebars in the stem. My bike has a compression fitting at the stem similar to the seat post. Your headset parts look the same, but my stem doesn't have a center bolt.
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