I remember when I went from a triple to a double on my 105 stuff and never had the shifting "quite right" but it was rideable (it made mario pretty mad though... stupid engineers).
I assume you've read and understand how to properly adjust the FD, but in case...
http://www.parktool.com/repair/readhowto.asp?id=75Chances are, if you're only "feeling" two shifts, you have an issue with cable tension. If you don't feel those 3 independent clicks then the derailleur isn't pulling on the cable hard enough to activate the mechanism. If you get it too tight though, you're shifting lever force will be noticeably difficult right away.
Switching to a double won't really "solve" the issue either since adjusting it is adjusting it. The chain won't know that there are only 2 rings there vs. 3. I def recommend looking into a double, but more for the weight than the usability.
I'll bring my cable pullers (3rd hand) by tomorrow if I get a chance to stop by your office (I'll be faxing that thing in the Union). It may seem daunting, but generally on an older setup if I can't get it to sort itself out with the 1st cable adjustment, I'll completely re-cable and re-house that system (perhaps leave the housing under the bartape if its routed that way so I don't have to retape the bars). Reason being, if you constantly pinch and repinch the cables, a divot forms and the cable will tend to "slip" back into its comfy zone. Not to mention the cable gets way weaker. If you decide to re-cable, I'd also recommend popping your FD completely off and cleaning it as well as the area where it mounts and then let it completely dry. Sometimes the grime causes issues too.
On a triple, its also beneficial to run barrel adjusters. Some people like them all over, but I never use them on doubles (too much weight lol).
Lastly, on some of the higher end systems you should push the derailleur off of the limit screw while you turn it. I never did this before and on my RED group I bent the screw. I imagine this is on the insane groups mostly tho...