I know this discussion is now nearly 1 year old, but thought I would throw my hat in the ring anyway.
I completely understand that rules are rules, and these have to be followed during training, but I also believe it is healthy and appropriate to regularly question the rules, this is the only way things get improved and kept relevant.
Also, very interesting to see opinions from both sides of the Atlantic.

My observations:
1 Travelling with a load in backtilt position is to compensate for fork deflection and very little to do with load centres. As a load is raised, the forks will naturally deflect downwards, the amount of deflection proportional to the load. Back tilt needs to be applied to ensure that the load stays on the forks during breaking. The change in load centre due to backtilt will be negligable. Most reach trucks have tilting carriages with only a few degrees of backtilt. In fact tilting the carriage back will actually push the load centre forwards and upwards which would decrease stability. On a trucks with tilting mast (including counterbalance), tilting back would have a marginal decrease in load centre, but not enough to make a difference.
2 Travelling with empty forks on back-tilt doesn't appear to have any significant benefit. I can appreciate that getting in the habit of always applying back tilt when loaded and unloaded may have some merit, but I don't see any specific benefit when unloaded. The argument about severity of injury when impacting a leg or ankle does make some sense. I suspect this may be inherited from the auto industry bumper (fender) height studies. If this is the only reason for applying backtilt then surely the same benefit can be gained from leaving the forks level, but in a slightly raised position? Both would lift the tip of the fork above ankle height. To place the forks in backtilt above ankle height would require use of the lift control anyway, so why not leave the forks level and just use the lift control?
3 Correct parking position of the forks. Reading the HSE guidance notes (UK version of OSHA) the only reason for applying forward tilt when parking is to reduce the trip hazard. This only requires a small amount of tilt to compensate for the taper of the fork thickness, and then lowering until the fork tip touches the floor. Applying full forward tilt and then lowering until the fork carriage hits the floor and the chains go slack should be discouraged, even though this is how some accredited trainers I have spoken to teach parking.

Expanding the discussion out further, why should backtilt be applied when using carton or bale clamps? These devices do not deflect like forks do, so I can't see why applying backtilt whilst travelling would have any significant benefit. I can appreciate that the mass of these attachments has shifted the loadcentre forwards, but this should have been reflected in de-rating the trucks lifting capability. Applying a small amount of backtilt will not make a significant difference to stability. The only reason I can see for insisting on this is to make the procedure consistent with a forked truck....