A trick the LBS showed me on the first day was the blind clip-in. It has pretty much been my only method of clipping in:
1st the back of the pedal is always down (or should be once the bearings are worked in...)
All I have to do is put my toe up to the cleat and slide it forward into the pedal and it's like butter every time... yet to miss(when I used this tactic... I have missed many times just putting my foot down). I do notice the cleat I use to balance at long stops unclips very smooth, I will be replacing them soon too... been walking around on them too much.

the float of the pedal is good, it allows a general fitting of the cleat rather than a perfect fitting... as would be needed with zero float...
I often look down to align my foot with the pedal...

as for the start: try reversing the crank so as you start your clipped in foot is just forward of top, that should give you a good amount of forward motion to then clip in leisurely.