I can usually pop a high D out with the C key just fine. It's harder, sure, but it works. Helps if you have a high note bocal, or at least a bocal with better high note response than a lot of "daily use" bocals I know some people play on. If she's playing on a stock Fox C bocal (normal for a 222) that's probably not helping matters in the top end.
I don't know that widening the collar would help at all. Narrowing the tip maybe would.
My basic fingering for high D, which works fairly well with just the C key:
Pretty much the standard high D fingering.
If she's that advanced is there any chance of her affording maybe a used 220 or something? Might be time for more than a single key upgrade.
Are you able to play the high D on her setup?
M.M.A., D.M.A. University of Illinois at Urbana/Champaign: B.Mus. Lawrence University
Bassoon professor at University of Wisconsin Eau-Claire
Maker of the Little-Jake electric bassoon pickup and Weasel bassoon reeds