I own some cheap PI MTB shoes. Have ridden road in them for a little over a year; they don't fit that great, but they were dirt cheap and fit well enough for a while. . I wouldn't say their toe box runs wide.
I need a wide toe box, and have one fit wider than the other. I, too, have tried Sidi, PI, and Lake. Nothing fit. I tried Sidi megas and Wides in the Lakes. The Lakes were close, but the wide was too big all over.
Tried on the full line of Specialized shoes today, since I've consistently heard they have a wide toe box. Walked out with a good deal on a pair of last year's Pro Carbon shoes. Fit one foot perfect, and the other quite well. Haven't ridden them yet, but this is probably as good as I'm going to get without custom shoes.
Short story: I agree that the specialized lines do seem to have more room across the ball of the foot.