John,
The short answer to your question is yes, adding _switchable_ CP, and elevation capability, will make a substantial improvement in your mode VU and UV system.
The longer answer is, well, longer. First, many people work very successfully with linear antennas. If the satellite has CP antennas, they are willing to eat the 3 db mismatch, or the spin modulation dropouts if it has linear antennas. Additionally, you should have the ability to switch between RH and LH polarization if you are going to use CP antennas. The actual polarization can change markedly depending on the aspect of the satellite, and the difference in signal can be many S-units.
Studies have shown that you can do well without elevation control on LEO satellites, but you should have your antennas pointing 10-15 degrees above the horizon. There is a good discussion here of why this works, and how to do it: http://www.ew.usna.edu/~bruninga/rotator1.html You have plenty of gain from the antennas you mentioned, and this is something you can try with what you already have. Note that for higher frequencies such as mode-L and mode-S the antenna patterns are much too sharp, and you will need a full az-el installation.
You did not mention preamps. There is truly no installation, from the most basic to the most sophisticated, which will not benefit greatly from a low noise preamp. The universal and unvarying response is always "Why didn't I do this before? Doh!" It should be remotely mounted at the tower, though with a short run of good coax you can get by with one in the shack on 2 meters. ARR and SSB Electronics both have good units with RF switching to prevent "oops!" incidents. (I have assumed you have quality low loss coax such as LMR-400 or LMR-500 over a reasonably short run. If not, the mast mounted preamp will still fix the receive problem, but your transmit power may be badly attenuated.)
You may not agree, but I am certain you have heard the expression "Life is too short for QRP." (Or bad wine.) Well, you can get by, but "Life is too short to work satellites without a _good_ preamp!"
If you do the above, you may well be pleased enough you can stop here. However, probably the next step would be a full az-el antenna mount, followed by CP antennas if you want almost guaranteed AOS to LOS coverage, every time.
Hope this helps, and gives you a good starting point.
Alan WA4SCA