I second the 70's/80's road frame suggestion, particularly the earlier end of that spectrum. Even the ones that were higher-end and used for racing have more tire clearance than a modern road frame, and the ones a notch or two down the line have more. Alternatively, since such things have become sort of trendy not only in the fixie world but also in the rando world, there are getting to be a fair number of modern versions that are similar, from places like Rivendell and Velo Orange. Also, even the racier ones have less toe overlap than modern road bikes, partly due to a somewhat longer wheelbase but also due to longer fork rake. And it just so happens that the longer rake/lower trail geometry is particularly favored for randonneuring because it handles better with a front load. Something like an early 70's Raleigh International might be a good bet.
My rando bike is my absolutely beloved 1974 Raleigh Professional, which is set up as a fixie and which I've been riding long distances on for probably ten years. This isn't the best photo, but it was convenient: http://www.dillpicklegear.com/wp-con...-19-48_293.jpg
Unfortunately the steerer of the original fork broke a few years ago and I replaced it with what you see there, which has less rake. One of these times, I'll dig up another more like the original, because I liked the handling better and this one gives me a tiny bit of toe overlap with the fender.
FWIW, I commute on a Surly CrossCheck and it feels like riding a cinder block compared to my Raleigh, even when the weight is equalized with luggage. There's no comparison.
Alternatively, you could always use a White Industries eccentric hub, which would open up more frame possibilities since you could use vertical dropouts. My better half has one on a Ritchey Breakaway for travel, and he loves it. It doesn't slip and if anything it's even easier to adjust the chain tension than with a normal hub. Not the cheapest thing you can find, but a high quality and very viable alternative.