It seems to me you can do the job with two relays in series. To make connection at an appointed millisecond, a wetted reed switch is the 'start' device, and to break connection (bounce not an issue) a DPDT regular-old-DC coil relay, with the NC moving pieces shunted to GND during the sensitive time, so the fixed contacts only have adjacent-metal capacitance (not parallel-buttons capacitance). This makes a kind of TEE configuration, both arms of the TEE being switched OFF, and the leg of the TEE shunted to ground, when you want to keep signal from leaking through. I'd consider using a second coil for energy storage, to give the DPDT relay a strong kick at the right time. Neither a reed nor a leaf-and-button relay is particularly reliable at opening when you power it down, it would take a rather odd kind of core to reliably demagnetize on the millisecond mark. Turning ON, though, under applied power, you can calibrate.