Toe overlap is not uncommon, and can result from a number of factors. A bigger frame may not help, but it might. If the ball of your foot is over the pedal spindle and you get overlap even at speed, you need a different bike. If the overlap only happens when turning at walking speeds then you either learn to live with it or look for a bike with more trail (like a touring bike).
My inseam and yours are nearly the same. My Fuji is a 56cm. If Fuji measures their cross bikes the same as their road bikes -- center of the bottom bracket to the top of the top tube -- then I think it's very likely the 52 is too small for you -- since it's the same size as a 50 or 51 from other manufacturers who measure center to top.
In my estimation there's nothing worse than a bike shop that "makes it fit" in order to sell a frame size they have in stock instead of ordering the correct size. I'm not saying that happened here, but everything you've said indicates a fitting problem.
I'm looking at the geometry chart for that bike. The 52 is a pretty small bike. The the top tube on the 54 is only 10mm longer than the 52's, but that might be enough to clear up the toe overlap. The 56's is 10mm longer than that.
Did you try the 56 he had in stock? If it was too big, in what dimension(s) was it too big?
RichC
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Training: 2002 Fuji Roubaix Pro (105 triple)
Commuting/Daytripping: 2001 Airborne Carpe Diem (Ultegra/XTR, touring wheels)
Commuting/Touring: 2000 Novara Randonee (Sora/Tiagra/LX, fenders, lights)