Only a short question; I've noticed when flying a couple of the more stable light aircraft (e.g. Cessna 182) there's a very small but noticeable long period pitch oscillation when stick-free. I seem to recall it was around the 30 second mark, seeing a variation of a couple of knots or so.
Most longitudinally stable aircraft do that to some extent. It is generally assumed that angle of attack and forward speed are approximately constant, and that there is a slow exchange of kinetic and potential energy around a constant lift (ie product of lift coefficient and square of velocity). Using this assumption and a bit of basic oscillation mechanics, you can model the period of the phugoid as PIE*SQRT(2xV/g).
That's assuming that there is no damping of the oscillation. Sometimes the oscillation can be divergent which can be quite interesting, but normally it is convergent and of such long period that the pilot is able to control it easily.
It is caused by small changes in tailplane incidence causing the centre of lift to move. With rearward CG the moment between lift centre is greater so the oscillation is more pronounced - as you have noticed.
I haven't heard of it being due to slack in the control runs. I have, however, experienced marked pitch oscillations on some aircraft while under autopilot due to a small amount of play in the elevator control runs causing the ap to be very slightly dephased from the elevator. However, this is not a true aerodynamic phugoid and could best be described as a pilot induced oscillation.