My Sony NEX-3 (first model) does not have the Electronic First Curtain Shutter feature, so when I use it for Moon photos, the close, open/close, open cycle of the focal plane shutter always adds shake to my pictures, even for 3-in-a-row actuated after a self-timer countdown. Is there a recommended way with this camera to get the effect of an EFCS-type vibration-free start of an exposure? Moon photos with an f/16 scope are about 1/25sec, so the "hat trick" is hard to do reliably. I suspect that beanbags draped over the camera and telescope are the best option short of upgrading to the EFCS-equipped NEX-5 series.
Are you getting proper exposures at 1/25? I think your blur may be more from overexposure than motion. Is the blur uniform (as if it were out of focus), directional along one axis (as if you were panning), or multi-directional (as if you were shaking the camera)?
I am assuming you have the motor drive on the scope engaged, but it may be introducing more vibration than the sky motion it is eliminating for the short Tv you are using. Even at 1900mm and with your APS-C size sensor any Tv over 1/5 second or so should be acceptable without the motor drive engaged.
I normally shoot the moon @ ISO 200, f/8, and 1/125. And that is using an EF 70-200mm lens (plus 2X converter) with only a 77mm objective on an APS-C body. Keep in mind telescope and camera lens nomenclature are different. A 1900mm, f/15 telescope does not necessarily correspond to a 1900mm camera lens stopped down to f/16. In a telescope the f ratio has more to do with the scope's field of View while the aperture is the diameter of the objective. Your camera's view through the Meade 125-EX should be much brighter than mine through the EF-70-200. How much the T-mount adapter chokes out some of the light from the scope is an additional variable, though.
Links to NEX-3 Moon Shots