How to accurately abbreviate solvents?
Ancient IUPAC literature

The IUPAC Interdivisional Committee on Nomenclature and Symbols states in recommendations from $1979$, Use of Abbreviations in the Chemical Literature,


  Since the style in which abbreviations are given (e.g., capital letters or small letters,
  with or without full stops) often depends upon well-established practices that vary widely
  from one journal to another, IUPAC does not recommend a specific style for general use.
  
  DOI: 10.1351/pac198052092229, archived version: here.


This means there is no one general guideline. You may compare this to units which are to be written, without exception, in upright Roman. (ACS Style guide does recommend Italic for molality $m = \ce{mol / kg solvent}$ but IUPAC disagrees.) 



The IUPAC–IUB Combined Commission on Biochemical Nomenclature (CBN), in $1967$, set forth a document of revised tentative, i.e., provisional, rules. Abbreviations and Symbols for Chemical Names of Special Interest in Biological Chemistry does not list $\ce{DMSO}$ specifically, however does mention the similar $\ce{EDTA}$.


  7.$\ $Miscellaneous Compounds
  
  7.1 The following abbreviations are permitted; although they are fairly common, they should be defined in any paper if it is thought that readers might be unfamiliar with them. Some abbreviations are taken from the list published by Annual Review of Biochemistry.
  
  [---]
  
  
  $\ce{EDTA}$ – ethylenediaminetetraacetic acid (or acetate)
  
  
  DOI: 10.1111/j.1432-1033.1967.tb00070.x, archived version: here.


The above article mentions $\ce{EDTA}$ only as a separate compound, and is written once, exclusively in upper-case upright Roman.



Summary

Disclaimer: What follows is mostly personal opinion, and should be treated accordingly. It is a summary of my present understanding.


There really is not a recent IUPAC document discussing this topic.
IUPAC does not enforce a ubiquitous principle upon which rules of abbreviations are formed. Abbreviations should be used as rarely as possible, defined where possible, and the specifics depend on the field, journal, and purpose at hand.
That said, some rules exist. For instance, most new organic compound abbreviations should derive directly from acceptable full names set forth in IUPAC's $2013$ Blue Book.
If an abbreviation of a compound, such as $\ce{DMSO}$ or $\ce{EDTA}$, is applied in chemical formulae, they should be written in lower-case upright Roman. A non-exhaustive list of exceptions is listed in IUPAC's $2005$ Red Book, section IR-4.4.4, paragraph $\mathrm{(vi)}$.
The following cited quotation from the same paragraph is very confusing.


  Abbreviations for solvents that behave as ligands should also be in lower case letters [e.g. $\ce{dmso}$ for dimethyl sulfoxide {(methylsulfinyl)methane}, $\ce{thf}$ for tetrahydrofuran]; the practice of capitalizing the abbreviation of a solvent when it does not behave as a ligand is strongly discouraged as an unnecessary distinction.

I am fairly certain it means the following: If a collection of atoms attached to a central atom does not behave as a ligand, you should still use lower-case abbreviations when composing a chemical formula. Unless exception. This does not mean nor imply you ought to use lowercase when discussing a solvent on its own.
The formula $\ce{[CrCl2(dmso)4]Cl * dmso}$ seems correct to me. Not entirely sure if you could also use $\ce{[Cl2Cr(dmso)4]Cl * dmso}$.
I would include both options in the glossary but with a footnote. Mention that uppercase for $\ce{DMSO}$ is generally used the compound itself, lowercase is reserved for compiling a chemical formula. This might be overkill; if you prefer one, I would go with including only the upright version. But again, if space is not an issue, add both for maximum clarity.