Changed Op-amp, now signal is not centered
The input bias current of the AD8051 might be as high as a couple of micro amps and this doesn't sound much but, through a 1Mohm feedback resistor, this will generate a dc error of 2 volts on the output. Note that with the +input seeing a DC resistance of about 5kohm, the same bias current will produce an error of about 10mV. I would suggest equalizing resistances in both inputs but you are going to start to run into noise problems with so many 1Mohms in your circuit I suspect.

Try something more like and AD8605 (input bias current less than 50pA). Alternatively consider the non-inverting topology: -



Not shown is the electret bias resistor of 10kohms and, also, Rin is not needed. The non-inverting input is biased at mid-rail by the two 100k resistors and these, for a device like the AD8051 can be as low as a couple of kohms thus ensuring bias currents don't create a large offset voltage. RF and R1 set the gain and a gain of 1,000 can be achieved with R1 = 100 ohms and RF = 100,000 ohms - this means the feedback resistance is one-tenth of what you had and the offset it introduces will accordingly be one-tenth at about 0.2 volts on the output. Ci in the feedback area will need to be much bigger than 0.1uF because R1 is now only 100ohms - something like 47uF. Ci on the input leg can be 10uF.