If you had a big enough flash drive (or writable network location, like another CIFS-capable computer on the network), you could extract one file at a time from the archive, then delete the file from the archive, using the (~20GB free) "other space" as the temporary/scratch location. Every archiving utility I've ever worked with can specify an alternate temporary location.
This example script uses 7-zip (as well as grep and sed):
FOR /F "delims=*" %%f IN ('7z.exe l "%ARCHIVE%" -slt ^| grep -B1 "Folder = -" ^| grep "Path = " ^| sed "s/Path = //"') DO (
7z.exe x -y -o"%DEST_DIR%" -w"%SCRATCH_DIR%" "%ARCHIVE%" "%%~f" >NUL
7z.exe d -w"%SCRATCH_DIR%" "%ARCHIVE%" "%%~f" >NUL
FOR %%g IN (%ARCHIVE%) DO @ECHO %ARCHIVE%: %%~zg
It is functionally correct, though I did not attempt to create a file too big to extract on my computer just to test it.
You could also temporarily compress some files on the hard drive that you know you won't need during the extraction process (like, say Office) to free up just enough space to extract the files, then reverse the process once extraction is complete.