Hi Elli! great to hear from you, and also to learn of another major 
project diving into the warm TEI P5 water...

I'll just comment briefly on a few of the specific issues you raise 
below -- I'm sure others will want to chip in too

1. dimensions  : as of P5 1.4 you can now use a generic <dim> element 
within <dimensions> which may be more appropriate/simpler for recording 
arbitrary bits of text-bearing-object-measurement than <measure>

2. <objectDesc> the purpose of this element is precisely as you say to 
document the whole of the text bearing object (henceforth TBO). You can 
(obviously) tweak the domain of the values for the @form attribute to 
suit your project's needs. Within that element you have the choice of 
paragraphs, or  a grouping of matters relating to the carrier followed 
by a grouping of matters relating to the inscription itself.  If your 
full description refers to both support and supported, and then maybe 
goes on to describe the other aspects in more detail,  then I can see 
the case for a separate overall <summary> or <desc> as first child of 
the <objectDesc>. But I can't as yet see the case for a new <object> 
within <supportDesc>, since this would duplicate the intention of the 
<objectDesc> itself.

3. @ref and @ana both take anyURI as values and thus either of them can 
point within the same file or elsewhere (we have some guy called Durand 
to thank for that). It might be a good idea to use @key however if you 
want a generic "controlled code which is equivalent to the content of 
this element" type attribute. If you want to invoke a taxonomy of 
material types, then @ref or @key would be appropriate. @ana implies 
rather that some kind of analytic interpretation has been applied so one 
might rather fancifully say <cake ref="# madeleine" 
ana="#swanns-way">small proustian pastry</cake>

4. I don't follow your comments on @cRef and global attributes, and 
James tells me he thinks there may be a misunderstanding here.  @cRef is 
a rather specific  way of doing certain kinds of pointing; it should not 
be global. It relies on a homegrown addressing system which was really 
cool in P2 or P3, but looks a bit strange now we have xpointer ... @key 
and @ref are not global either: they are inherited from membership in 
the att.canonical class. James' proposal was, I think, to add <material> 
and various others to that class.

Looking forward to hearing about fakes. You might like to check out the 
new material on <certainty> in that connexion...