I too love my 45# recurve for bowfishing.
The one I have is old and solid fiberglass with no mounting holes at all.
I had to rig it so I could mount my reel, so I'll upgrade in a few years toa modern take-down recurve of the same weight that will accept accessories more readily.
The recurve's main advantages are asmooth draw,the ability to snap-shoot very quickly, it's very light to carry and you don't have to draw back all the way if you are shooting where there is a decent chance you'll hit a submerged branch or rock.
Oniedas (sp?) are also very popular with bowfishermen. With their smooth draw and single string they provide minimal cables for the bowstring to become entangled in causing snapback.
http://www.amsbowfishing.com/bowfishwarning.php?osCsid=58c01df9e8d12b74418fcc8e 2d455a33
Although I have not shot one, I hear there is a trick where you can prop the lower limb against your leg when at full draw to take the tension off so you can hold longer.
Compounds are used too. Useful for long and deep shots at big fish, they have their advantages too. Since they are heavy to hold all day, they are not my preference, but they'll get you plenty of fish. I've found that compounds with medium and hard cams take too long to draw, and you may miss shot opportunites. Sometimes the fish is only visible for seconds, and he'll be gone by the time you draw, wait for the cam to roll over, anchor, get a sight picture, and are ready torelease. If you want to use a compound, I'd recommend round wheels or soft cams.