First recommendation: rate your Tri-X at 1250 or 1600, and develop
yourself, in Diafine.

Second recommendation: get some Neopan 1600, Delta 3200, or T-Max P3200,
rate it at 1600, and develop for that EI (or develop in Diafine, which
will mean shooting at 1200 to 2000 -- I don't have my Diafine table
handy to say which is which).

Third suggestion: if your camera will permit, get a faster lens.  In 35
mm format, lenses of f/2 or faster are quite common, even in rangefinder
cameras, and you can buy a used Spotmatic with 50 mm f/1.4 for under
$150, ready to shoot.  The meter won't be much good at that light level,
but the camera will work fine if you know your exposure.

You could experiment with color/B&W infrared film in the camera. Use some
unexposed but processed E6 film to build a filter to cover your flash,
basically it cuts out the visable spectrum leaving the infrared to light up
the scene.

 Use a faster film.  Dan

  I also agree with those suggesting a faster film.
Understand that there really is no such thing as increasing
the film speed by increasing development, i.e.,"pushing".
What you are doing is increasing the contrast. The low
exposure end of the film curve, called the toe, has lower
contrast than the rest of the curve. When you underexpose
film much of the image lies on this portion of the curve so
increasing development will increase its contrast making it
more printible. Of course, it also increases the overall
contrast so any highlights falling on the normal exposure
part of the curve will become very contrasty and require
burning in to prnit.
   Below some point the film just doesn't record anything.
This limit is a bit less than two stops from the ISO film
speed. No matter how much development you give the film
nothing will appear in this region except increasing fog.
The ISO method of measuring film speed has very little
safety factor. It gives just about the minimum exposure that
will result in decent shadow detail. In fact, many
photographers find somewhat more exposure improves the tonal
rendition of the iamge due to greater shadow detail.
  It sounds like you are working under very difficult
conditions. I've done a lot of available light work myself
and have experienced the empty shadows you are getting. The
only answer is to use faster film or find some way of
increasing the exposure.
  Some developers yield maximum shadow speed. These are
mostly Phenidone containing developers although all
Phenidone developers are not equal. The best "pushing"
developers, that is, the ones which will give you the best
shadow detail with under exposoure are Kodak T-Max or T-Max
RS, Kodak Xtol, Ilford Microphen.
  Develop your own. You have control that way. A good rule
is that no pro lab knows what its doing no matter how good
its supposed to be. :-)