Gotta disagree, I think the Warmoth Standard Thin is the nearest to the Fender Modern C.
All the other Warmoth shapes are quite different - the Boat, Fatback and '59 are bigger than the Modern C, the Clapton and SRV are similar to their Fender equivalents, the Wizard is like an Ibanez and the Wolfgang is, I suppose, similar to a Peavey Wolfgang (or Music Man EVH/Axis).
If you think the Standard Thin might be a bit too skinny, I'd suggest the '59 Roundback. It's chunky around the 12th fret but not too deep at the nut.