I have played Pooh Sticks with my kids on numerous bridges, including the original one in located in Ashdown Forest in East Sussex (the "Hundred Acre Wood") where my great uncle lives.
This does have great potential to go down so many theoretical rabbit holes in good BPL fashion. In addition to the hydrodynamics that you mention (which might favor a low density object), remember that drop time is an element as well. A feather would move at the velocity of the water surface (i.e. faster than deeper water) and be pretty immune to snagging on a rock, but would take longer to fall to the water's surface.
First, to bang out the simple physics calcs, here are, for various heights,
height (ft), time (sec), velocity at end of fall (mph)
1 ft, 0.25 sec, 5.5 mph
2, 0.35, 7.7
3, 0.43, 9.4
4, 0.50, 11
5, 0.56, 12
6, 0.61, 13
8, 0.71, 15
10, 0.79, 17
12, 0.87, 19
16, 1.00, 22
20 ft, 1.12 sec, 24 mph
For most objects, just use the above times, but I've included the velocity at the bottom (ignoring air resistance) so you can assess if you need to consider air resistance. A human, body, something routinely ejected from perfectly good airplanes in the sport of skydiving, fall about 135 mph, so if playing Pooh Sticks with a human corpse, you may safely ignore air resistance effects at these low speeds. Here are some terminal velocities gathered off the web:
Skydiver: 134 mph
Baseball: 74
Golfball: 72
5 mm hailstone: 31 mph
Ping Pong ball: 20 mph
2 mm rain drop: 20 mph
parachutist (open): 11 mph
Feathers are going to vary a lot, but are slow enough to measure easily with a stopwatch.
The last (and most helpful) datapoint is the velocity of the stream. Sure, I don't know your stream, but a lot streams, rivers, and creeks travel at about 5 feet per second – about 3.4 mph – a brisk walking pace.
