Origin of increased noise in BF862/OP27 charge amplifier
First, JFETs usually have input voltage noise of ~nV and current noise of ~pA. In your case current noise will dominant.

Second, you are running the BF862 in ohmic region, which will degenerate it's noise performance. BF862 was designed to run near Idss.

Third, it looks like that the stability margin of your circuit was not enough. Which means it has more noise gain than expected. 

I think a simple MOSFET input OPAMP would do a better job than the JFET/BJT OPAMP composite amplifier. And, remember to make guard rings around to protect the input traces.