I got bored and frustrated (no weapon-making metals present unless I went into the underground, which I wasn't planning on doing without a military) with that fortress and abandoned it. It had been two years and no more fish migrated into my area, I'm pretty sure none would have. I'll just start a new one in a more ideal location and hope that I get lucky again with those elves.
Insofar as the caverns, a tactic that I use which has not failed me (while strictly maintaining it) is digging stairwells down to break into a reveal the caverns
usually from the top (i.e. unroutable between caverns and fortress by ground tiles alone, and if I happen to stairwell into the walled side of a 1Z-high section, I could have channelled out the stairwell access and capped it) then send a second branch vertically down through an appropriate mass of cavern wall to discover the next one down. If I like the look of any resources that aren't floor-level, I can build my own walkways (or alternate tappings into the system) into that area (further expanding my visibility). So far, nothing has flown up onto any of the walkways I'm building.
Occasionally, of course, one finds that the vertical shafts already did punch through a cavern layer in the midst of a rock pillar.
(The latest fort, I've not intentionally breached the caverns, and not done any such exploratory actions but I managed to plan the lower two levels of my bedroom zone such that it intersected the top of some particularly tall caverns[1]. Currently they're wide open to anything that might fly, or climb up walls, but nothing has tried. I'm taking some time to wall and floor it off in the appropriate variety of stone (to fit what would have been there if it wasn't cavern) and may even install some windows in some of the gaps.)
But from the fish-taming POV, yes, you're probably as well starting over.
[1] The bedroom zone goes maybe 4Zs up into the mountain, from the level of the plain that I dug into it from, and is 10Z deep in total, so that's 5 and 6 Zs below 'ground' level. Which is the highest I've ever seen caverns, but then I've not embarked in such a disjointed place before. The embarkation map showed almost solid "8" and "*" and worse cliff edges over the
entire zone, despite the NE 9x9 square being entirely plain (with a few ponds, but not enough to give such indication of undulations), so maybe the site-chooser was picking up on cavern topology...