Noise pickup in fully floating circuit
The transformer inevitably has capacitance between primary and secondary windings and, any common mode signal fluctuations from the "battery powered floating bias current source", will cause a differential signal to be delivered to the single-ended pre-amp via the inter-winding capacitance. 

The 1 Mohm resistor provides an alternative shunt path for these common mode signals and thus you see noise reduce. If your pre-amp were differential and balanced you might find that things improve significantly.