If shallow depth of field is essential to the story and the visual style you're (collectively) going for then it's worthwhile investment, but shallow depth of field is only one look, not the only look.
A bigger problem seems to be that you and the DP seem to be pulling in different directions. She has one set of priorities, you have another. Why are you so against the adapter? That's not a rhetorical question, there may be good reasons - if your DP wants such a shallow depth of field, you'd better hope she has a really good focus puller working with her. I'm not a big fan of the adapter look myself, but then being a long time Kubrick/Welles fan I'm partial to bit of deep focus. Personally I think it's way overused, (in the way that 70's movies overused zooms) in some cases making every shot look like miniature; check out this example of too much adaptorising
http://www.vimeo.com/420617. There certainly is a cult of the 35mm adapter and many believe it's the default position, rather than one option now available.
However on a low budget shallow DoF can have a few serious advantages. It does do a little to take off the video curse. It means you don't have to worry about background composition and clutter as much which tends to make shots look better composed than the same shot with deep focus. It is a look people associate with a bigger budget production (
Tadpole,
Celebration,
28 Days Later et al all made a virtue of the low budget grungy DV look, so it wasn't an issue). For an actor centered drama shallow DoF can be useful to direct the audiences' attention where you (as director) want it.
On the other hand, if you really don't care, it might be better to defer to the DP - I'm reading a little more "what's the big deal?" in your posts rather than "this is
wrong for the movie". That doesn't make you a bad director - plenty of great directors are not particularly technically minded but those directors defer to their heads of department. But at least, ask her WHY she really wants an adapter, what is the look she's going for. If her response is simply "it makes it look less like video", "It's what everyone else is doing on HDV" or "It'll make my job easier" then frankly she's not worth $350 a day.
when Nancy Schrieber shot
November, 35mm adapters weren't really as widespread as they are today. Had she had the option, she may have chosen to use one. But as you say there is a LOT more to that movie's lighting than the depth of field.
Maybe you and the DP could rent an adapter and shot a couple of tests to see if it's going to work for you.