How old are your cleats? I'm running X-Series pedals, and the first part of the cleat to wear out around the 7000 kilometer mark is near the two springs used for retention, they grind a slot into the aluminum spring housing plate resulting in play similar to what you describe.
Just to be sure, I checked the two pairs of cleats and... the left retaining plates both have little groves in them - at the back of cleat and opposite side to the float adjuster where as both right cleats are much more even! They are not massive, but there is a definite different from left to right.
What makes me wonder though, is that with the new pedals I initially used them with old cleats for a bit (~200-250kms) and noticed that play. Then I installed new cleats and the play was still there - the pedals have not been worn by the old cleats or anything like that.
It may have something to do with bringing the shoe closer the the BB as well as moving the cleats further back a bit a couple of moths ago. I do think though that the sole of my shoe is not quite level on the left side as even the float on SPD-SL cleats is a bit different from left to right - but knowing me I could just be imagining. Shoes are Spech Pro 2010 btw.
Thanks for that ECT - I have sort of noticed the groves before but did not pay much attention to them. I also checked previous sets of cleats and they don't have the grove as bad as the above two cleats.
I will stick with the 105s for the time being and see how they go, but I think SP specific shoes are on the cards if I am to use them again.