Truly an interesting thread, very informative answers.
Buzz... I do like the answers regarding "acting" and such, along with the suggestion of adopting some stylings from singers you admire. I'm trying to work on my own vocals and suffer similarly, and know plenty of others with the same issue.
I'm thinking a deliberate attempt to "exaggerate" might be an effective suggestion while practicing.
Seems you did relate strongly to the suggestion you are not having fun. You might look deeper into that one. I imagine you actually are having fun, maybe just not as much as you'd like. Might be a simple matter that you are too self-conscious and worried about control or perfection.
Couldn't it be said that controlling yourself also controls the audience?
I'm only guessing here: as soon as you hit the "record button" at home, everything goes to hell in a handbag? Common.
I think Mike's suggestion to sing and sing and sing comes into focus here, it needs to become second nature and something we don't fuss about within ourselves. It must be given freely.
While I realize I'm rambling... I'll also continue with a bit of psychology. Are you in front of the audience to fulfill your own personal need to be heard, or are you there to fulfill the desires of others..aka the audience's need to be entertained? Whatever the answer is,(and it will be one of the two) the directional flow of your energy is critical, as it must flow from you to the crowd before you receive your just desserts. Right?
Give energy.

-gary