Do a factory reset and don't install any apps, whatsoever, for at least a day or two. Try it completely stock. See if that fixed your problem.
After that, slowly install each app and start to "wade" into them and see which one is causing an issue.
Generally, an app that doesn't have very many downloads is written by a dev that most likely writes its apps poorly to begin with. Obscure apps that are more for novelty, generally are not a good idea. See if you can pick those apps out before you reset.
You may also have the 50% without signal bug. Go to Settings, About phone, Battery Use, and then Cell Standby. Does it say "Time without signal" and a "50%" next to it?
If it does, you have the bug. No permanent fix, but if you ever reboot your phone, put it into airplane mode for a few seconds and then take it back out. The percentage should go down slowly. If you are next to a charger, plug it in the charger and then do the airplane mode thing. Then take it off. Putting it on the charger resets these stats so it should be back down to 0%. Actually, it shouldn't say "Time without signal" at all, unless you spend at least a second...without signal.
Another thing to do is dial *228 and do both the 1 and2 option to reprogram your phone. It should connect you to the nearest tower, which obviously helps both battery life and call quality.