Carp...The river north of the Bissel is basically shallow, however not too far up river is the mouth of the Farmington river, there in that area you will find some deeper water. As far as going south from the Bissel, I don't know it that well but think you have to go down quite a ways to Hartford area to find water. (most likely you are trying to avoid the wethersfield cove launch Nazi ! )
If you wanted to try the mouth of the farmington, there is another boat launch that I will suggest, it is located in Windsor behind "Bart's" on rt 159 right were 159 goes over the farmington river.
I suggest you try it sometime, head downriver and explore a bit, you can always go upriver at some point if you like the area.
I can't help you with the Enfield dam area, but that would be strictly shore fishing I would guess, maybe someone else can assist you on this.
As for keepers up this way the past week, the water has been so low I have not even tried, and I know of several people who felt the same. Maybe someone got one or two, but I haven't heard about it.
The CT river looks like it will rise a bit this weekend, check this link.
http://newweb.erh.noaa.gov/images/ahps2/hydrographs/hfdc3_hg.png
Remember this is Hartford area and not exactly Windsor.
Any questions feel free to message me.
diggadave, The Bissel bridge is under I291 on the Windsor side, just thought you might like to know.