So, for posterity (and/or time travelers from the past), here's what I did to extinctify the source-control bindings:
0) Created a new folder to house a copy of the polluted (source-control-bound) files.
1) Copied all the latest code to there, except for the source-code-specific files (I copied over all *.resx and *.cs files, also Platypus.sln, Platypus.csdproj, and Platypus.csproj).
I did NOT copy over:
mssccprj.scc
vssver.scc
Platypus.csdproj.vspscc
Platypus.csproj.vspscc
Platypus.vssscc
Platypus.csdproj.user
Platypus.resharper.user
2) Stripped this entire block from the the Platypus.sln file:
GlobalSection(SourceCodeControl) = preSolution
SccNumberOfProjects = 2
SccLocalPath0 = .
CanCheckoutShared = false
SolutionUniqueID = {D6B21FF1-3534-49C0-8E4E-EE1FA496648E}
SccProjectUniqueName1 = PDAClient.csdproj
SccLocalPath1 = .
CanCheckoutShared = false
EndGlobalSection
3) Stripped out the "SAK"sy stuff from Platypus.csdproj, so that this:
<ecsharp>
ProjectType = "Local"
ProductVersion = "7.10.6030"
SchemaVersion = "1.0"
ProjectGuid = "{CA63566E-76DE-4EE5-8292-71EBF90A9AC9}"
SccProjectName = "SAK"
SccLocalPath = "SAK"
SccAuxPath = "SAK"
SccProvider = "SAK"
>
. . .
</ecsharp>
...became this:
<ecsharp>
ProjectType = "Local"
ProductVersion = "7.10.6030"
SchemaVersion = "1.0"
ProjectGuid = "{CA63566E-76DE-4EE5-8292-71EBF90A9AC9}"
></ecsharp>
4) Removed the four"SAK" entries from the Platypus.csproj file, which had:
<propertygroup>
<projecttype>Local</projecttype>
<productversion>9.0.21022</productversion>
<schemaversion>2.0</schemaversion>
<projectguid>{0848BFFE-EC53-4CC2-89AC-DF02C06585C2}</projectguid>
<sccprojectname>SAK</sccprojectname>
<scclocalpath>SAK</scclocalpath>
<sccprovider>SAK</sccprovider>
. . .
<sccauxpath>SAK</sccauxpath>
</propertygroup>
That pretty much did it.