Jeff:
There are tons of examples overseas where crossing holes work, or at least, to the point of hitting a tee shot across the previous green.
95% of the successful examples involve one of the holes being a par-3. When the hole is a par-3, it's much easier to predict the traffic flow and timing of the traffic. If you've just finished a par-3, you know that the group behind you is still on the tee, so the green is probably going to be wide open for you to back up and hit a tee shot over it ... as long as you don't have to wait on somebody in the fairway. Slow play makes crossing holes tougher to execute, and of course, crossing holes tend to cause delays in play, too.
The only par-4 crossover I've seen in America in the last 20 years was for two holes at Oak Tree Country Club ... the second course at Oak Tree. One hole is like the 18th at the TPC Sawgrass, and the other hole runs the same direction down the opposite side of the pond, so Mr. Dye made the tee shots cross over, over the lake. No traffic problems there, as all the traffic crosses over behind the tees on the way to the fairway.
I've drawn crossover solutions for a couple of holes on projects we've made plans for. One was a resort in the Turks & Caicos ... the other was a redesign in Japan. Neither of those projects got built, though, so my first crossover that sees the light of day will be the one at Tara-Iti in New Zealand ... where the tee shots for the par-4 3rd and par-5 5th cross at 90 degrees, about 75 yards in front of the tee, in full view. It might occasionally cause someone to wait a minute or two on the tee, and admire the views of the ocean, but the course is not going to be very busy so it's no big deal.