This forum is not very useful, I'm afraid.
Nonetheless, here's how I solved this problem:
<!-- Check out the binaries from TFS--><MSBuild.ExtensionPack.VisualStudio.TfsSourceTaskAction="Checkout"ItemPath="$(BinaryPath)"Version="2010"WorkingDirectory="$(SolutionRoot)"/><!-- Add the files from the drop folder to the Build Agent working folder. --><CopySourceFiles="@(FilesToAdd)"DestinationFolder="$(MyAbsolutePathProperty)$(WorkSpacePath)"OverwriteReadOnlyFiles="true"/><!-- Check in the updated binaries to TFS --><ExecCommand="$(TF) checkin $(BinaryPath) /comment:"***NO_CI***" /bypass /noprompt /recursive /override:"Auto-Build: Version Update" "WorkingDirectory="$(SolutionRoot)"/>
$(BinaryPath) and $(SolutionRoot) are passed in from the calling workflow. @(FilesToAdd) is the enumeration of the files in the Drop Folder (also passed in from the workflow). I used the /bypass parameter of the tf.exe command to override the gated builds that would have otherwise been triggered by this check-in. It's also the reason I didn't use the Extensions checkin command. As a matter of fact, I could easily have done this whole thing without the extensions altogether.
If anyone wants the whole script, just message me.
jr