Better beat mapping in logic

I like to build cover versions of songs by beat mapping the original, then playing all the parts over the top until it's at a point where it sounds good without the original. Obviously beat mapping is crucial for this to work, but I have never had any real success and always run into timing issues. I can get approximate mapping either using transients in the beat mapping track, or recording a midi click track and syncing up the beats that way. The problem is that transients don't work well on full mixes, and my timing is nowhere near good enough for the click track to be much use - I still get terrrible flamming or syncopation on drums etc. Another problem is that the beat map is terribly sensitive to changes - I always have to start at the beginning and progress all the way through until it's matched all the way through. If I go back and change one single entry, it throws the timing for the whole of the rest of the track, so you have to do it perfectly first time, rather than just bumping up the tempo until the next matched hit point (that's what it does visually, but it wrecks the actual alignment).

Given that logic can do such amazing tricks of precision with flex editing, I'm quite disappointed that it can't handle the apparently simpler task of beat matching. Is there a better way? A plugin or some dedicated app? Does Cubase's beat detective do a better job?