Hi, AUDIO FREQ
The gxl3000 is a reasonable microphone for its price, but it has a rather bad signal-to-noise ratio due to the jFET transistor used, which has a high input capacitance, about 30pF. The bipolar transistor does not have an important contribution to the noise increase.
In addition the jFET is not properly biased. R10 should be removed and R9 replaced with an adjustable resistor (eg 25kohm), and a manual BIAS done. I would replace the jFET with something else (eg 2sk30a).
All this has been analyzed in detail several times by the group members, the scheme is quite generic.
However, without changing the capsule you don't get a radically different character.