Why were you using a 3" long tapcon screws to anchor one of those post bases? The base anchor plate is at most a 1/4" thick I believe and you only need to penetrate into the concrete about 3/4" or so. So a 1" tapcon would have done the trick and you would have had more success at actually getting it to screw in all the way. The 3" long tapcons are useless...you'll never get them to screw down all the way without stripping, and using them to secure a 2x4 is a waste of time.
I only use tapcons when I have no choice because I am afraid of splitting the concrete...like underneath a toilet flange. For anything else, and especially when I have to anchor something wide like a 2x4...I use a powder actuated tool...I bought it out of frustration, and it has been one of my most satisfying tool purchases to date. You can even get the cheapo units (under $50) that you strike with a hammer; I have been told that they get the job done.