Build a floor, it's faster and doesn't demand architecture
Yes, but it takes more stone.
I have had exactly
one fort in which I did not have more than enough stone[1]. My usual problems are of the "I need 1000+ more sandstone blocks" variety, more OCD in nature than game-breaking.
If you can wait (although admittedly it sounds like you can't) building an extra bridge or twenty helps train up your designated architect. To really speed things up (for the architect, or the masons[2] when it comes to floors) set down a stockpile of the appropriate materials and empower a dedicated army of haulers, when the first item(s) arrive there
then you set it to be built. (Don't shift-select bulk materials, but make sure that the distance to the material remains consistently low, ideally in single figures.)
Also, if you dismantle floors over a river, the materials are lost. (Not, as mentioned above, likely to be a problem... Unless you used spoilermetal bars for them. But it does leave an untidy set of materials lying on the riverbed, which my aforementioned OCD doesn't like...) Build a bridge and dismantle it later and the materials used will sit happily on the side of the bridged gap. Although possibly the wrong side.

The first thought I had (although the frozen river solution is doubtless the more correct) some sort of badly-assigned burrow so that all the fisherdwarfs were barred from going home to feed/sleep (although they
do break that restriction when desperate, I believe).
I was also reminded me of "Urist McHunter cancels Hunt: Hunting for Vermin for food" message.
My first thought when I had only seen the subject, however, was that Fisherdwarfs are
already insane. One reason why I tend to treat any fish-related skills as dump-stats and treating fish-type immigrants as the peasants (or secondarily skilled guys) that they would be if they didn't have any of the dark-blue tendencies.
HTH, HAND.
[1] And that one was a soily 40D with mucho-aquifer, and the very first one that, for want of something else to do, I actually learnt how to properly grow crops and started to not suffer from the problems from which my screen-name is directly derived.
[2] Ignoring for now wooden or metal bridges.