In the end, I used the TypeAttributeMoveTool utility, which is highly documented in the WHC and a few tech support articles. I wasn't exactly clear how to implment the tool in my situation, but I stumbled through it. This was my procedure:
OLD STATE:
wt.doc.WTDocument (defined IBA such as MATERIAL)
com.ptc.Agenda (MATERIAL is inherited, but doesn't apply to Agenda, of course)
com.ptc.Analysis (MATERIAL is inherited, but doesn't apply to Agenda, of course)
com.ptc.Bill_of_Material (MATERIAL is inherited, but doesn't apply to Agenda, of course)
...
com.ptc.Drawing (MATERIAL is inherited)
...
TEMPORARY STATE:
wt.doc.WTDocument (defined IBA such as MATERIAL)
com.ptc.Agenda (MATERIAL is inherited, but doesn't apply to Agenda, of course)
com.ptc.Analysis (MATERIAL is inherited, but doesn't apply to Agenda, of course)
com.ptc.Bill_of_Material (MATERIAL is inherited, but doesn't apply to Agenda, of course)
...
com.ptc.Drawing (MATERIAL is inherited, and Drawing_MATERIAL is a new IBA defined at this level)
...
Now the IBA exists on the com.ptc.Drawing twice - both as MATERIAL and as Drawing_MATERIAL. The MATERIAL IBA contains a value. However, the Drawing_MATERIAL IBA does not contain a value yet.
Execute the command:
windchill com.ptc.core.lwc.server.TypeAttributeMoveTool <typeName> <sourceAttributeName> <targetAttributeName> -u <userID> -p <password>
Such as:
windchill com.ptc.core.lwc.server.TypeAttributeMoveTool com.ptc.Drawing MATERIAL Drawing_MATERIAL -u wcadmin -p <password>
Now the Drawing_MATERIAL IBA contains the same value that MATERIAL contained. Therefore, we can safely delete the MATERIAL IBA from the top level wt.doc.WTDocument (after first removing them from the layouts).
FINAL STATE:
wt.doc.WTDocument
com.ptc.Agenda
com.ptc.Analysis
com.ptc.Bill_of_Material
...
com.ptc.Drawing (defined IBA: Drawing_MATERIAL)
...
and now my Agenda's, Analysis', and Bill of Materials' don't have the MATERIAL IBA on them anymore. And the Drawing_MATERIAL IBA contains the values that the old MATERIAL IBA contained, so no data has been lost.