If I understand your situation, you have a negative which is too high in contrast to print properly. If flashing doesn't work for you, then you may be able make an unsharp mask (unsharp positive of your camera negative) that would then be printed in a sandwhich with your camera negative to compress the contrast range of your camera negative. This would have the added effect of granting additional apparent sharpness within the print.

If you don't want to go to the bother of doing that, then you may want to return and reshoot the scene with your 4X5 and probably look to doing a pre-exposure of the film through a diffusion plate at a Zone III value (to support the shadow details) then follow that with a second exposure (without the diffusion panel) on the same sheet of film as the normal scene brightness would indicate.
The effects of this can be readily determined, for yourself, by assigning a value of one to a zone one placement, a value of two to a zone two placement, and a value of four to a zone three placement. Since additional stops of exposure are doublings of the previous value the zone three preexposure through the diffusion panel will have virtually no effect of added exposure at the higher zones.
This may still require a minus development (if the high values would be exposed too high). This would of course be determined by the metered values at the time of the exposure.
The effects of pre-exposure of the film can be observed in my image "Doorways" which is in the critique gallery. The scene brightness range of this image was on the order of 13 stops. Yet, the negative prints very nicely on grade two paper.
Hope that this helps. Good luck.