OK, you guys are going to get me going here....

I work for Pratt & Whitney aerospace, we manufacture turbine engines which use almost the same basic principals you are discussing. The problem with the taper is that it builds considerable amount of back pressure in the tube while accelerating the water. Jet engines accomplish this by having a minute (<10 micron) gap between the blades of the impeller (propeller) and the shroud housing (mailbox).
This kind of alignment and clearance is not possible reliably in a swing down mail box, and would likely be more expensive to engineer and create than it would be worth. Theoretically you could get away with a slightly larger gap due to the fact that you are working with water as opposed to our air, but I'd have to ponder that one a while, because the backpressure would also be higher, possibly resulting in a lower allowable clearance.
However, if you built a simple 2 or 3 stage compressor into the mailbox that was powered by the water force of the propeller, you might get some worthwhile results for a smaller expenditure. I tend to think you could simply blow a hole in deeper water or blow it more quickly at a set depth with a higher velocity. With a simple step-down mailbox you'll just get less water through it at about the same velocity due to losses around the shroud.
Hydrodynamics and aerodynamics are very different, so I'm not completely sure what a stage compressor might do in water, but I do know why the funnel shape doesn't work on a mailbox. Ramblings from an aircraft engine guy...I'll shut up now
Jason