Perhaps you could just pit/pond the grates in the dining hall and have the dwarves fill it up from there instead? That would remove the need to have the dangerous opening on the lower level.
IME (although I don't do this sort of thing often enough to be completely sure) you may have difficult with bucket-chain filling the underside without evaporation.
Perhaps something (converted from a "dig out" version that I've used in the past) with floodgates, like so...
# # #
# #^#
#__________________ ___________________#|#
###################_X_X__X____X________X_#
Fill the open-topped 1-tile pond to 7/7ths, then remotely open the floodgate attached to it.
7/7ths of water spreads into 2..3/7ths of water up until the second floodgate and can be filled up to 7/7ths.
Open that next floodgate, and 3x7/7ths spreads into 6x[3..4]/7ths (you could make it further, or open sooner, of course).
Continue until you're abutting the last floodgate, beyond which is the uptake point for the (simplified in this diagram) pump-stack.
I'm a little worried that the pumpstack will actually drain enough water out of the end to encourage evaporation, so it may need topping up (might be doable while the waterfall is in motion, with grate protection against bucket-dwarfs being swept in), but otherwise it should work.
Having a separately filled cistern off to one side (as per the "Water Input" part on that image) is possibly a little better, in that you can keep that topped up from whatever water source you want, and can engineer enough fullness beforehand and afterwards.
You can't build a 3x3 grid of grates because of the central one not being supported, but you could have the central spot still unmined (not a floating floor, but one on top of an unmined lower part). Also, I'd go a bit more than 3x3, for safety's sake, and perhaps go with the following aesthetic pattern:
+++++++
+#####+
+##+##+
+#+#+#+
+##+##+
+#####+
+++++++
# = grate, + = floor.
All the grates are supported, assuming the 'diamond four' floors are over unmined tiles (or, of course, supports... hang on, can a central grate be built on/immediately to the side of a support? ...that might also work! Try supports below where the floors are indicated, then grate the
whole thing over...). But you'd not have the same freedom to "volume-double" the watercourse while you're filling, without some very particular changes to that plan (water being filled from one side, eventually to lead into the collection bowl, or the central grated area funelling down into a Z-2 water-conduit).
This all needs experimenting with, but my current fort isn't conducive to that kind of meddling right now (other design pressures) and starting up a new one/subverting a different old one will take some time, so perhaps someone will be able to confirm/deny some of my suppositions.
(Graebeard's ninja reply also rings true, I suppose I'm used to "full water" systems. And my "problems" look suspiciously like Graebeard's "solutions", when looked at from his POV.
)