Wow, it's like I could have written this myself!
One of our customers is a higher-end restaurant chain, who also like to keep the lighting dim at night. Since every site has its own design "oddities", the lighting for the ID shot at some is also particularly tricky, between backlighting, small overhead pin lights, etc.
In the past we've generally used Panasonic SuperDynamic cameras for this purpose (CW or CP484 with SDIII, later CW504 with SD5), but there are instances where even these couldn't really get a good image... and as in your case, management is adamant that the lighting will not be changed to improve facial shots.
Their current spec is Axis P3384 cameras for all public areas, as the Lightfinder feature works very well with the overall dim lighting. There are a couple of instances where we use the WDR function instead, but for the most part the better exposure is more important than "pretty" balanced images.*
For ID shots, I find what usually works better than WDR, is to set them to Lightfinder, enable BLC, then create custom exposure zones using mid-grey-level objects that are under approximately the same lighting as faces will be once inside - door mullions work surprising well for this, or sometimes a bench or planter just inside the door.
I'd have to check, but I'm pretty sure I'm using a 1/60 minimum shutter speed on these - still get a little blur if someone is walking briskly, but since people usually come in the door and stop to look around and/or wait for a hostess, that's not a major problem most of the time. Most sites have a hostess stand right there, and we'll try to aim cameras so it's in or near the edge of the frame, so we get faces as people are talking to the hostess.
*What would really be ideal in this situation is if the camera could automatically switch between LF and WDR modes based on lighting level, while not changing day/night (or IR Cut) mode as we too want them to always be in color... but currently the only way to do this is to have it switch WDR modes based on using the day/night mode switch as a trigger. The problem I found with that is, when it switches to night mode (ICR out), then toggles LF on... the exposure suddenly increases enough that the camera soon goes back to day (ICR in), which triggers a toggle to WDR... which makes the image dark enough to trigger ICR out... and these cameras also have no adjustment for that trigger level (or didn't at the time), so the only way to counter the hysteresis was to fiddle endlessly with exposure settings. So I just set them all to LF and left it at that.