So you are willing to spend $75 just so you can run your SL-7900 downtube shifters with a 9 speed cassette.
Others have suggested going to a 10 speed cassette and using either the Altus or your 105 RD.
You could use the 105 and a 10 speed cassette probably save $25 while adding an extra gear.
Or get a 10 speed cassette and an Altus RD for the price of a Shiftmate.
John