In the middle of the belt there is 15mm of vertical movement whilst apply minimal force, alternatively I can twist the belt 40 degrees with some force. Prior to slackening the belt there was only 5mm maximum movement.
These results seem to pointing to the fact that temperature is causing problems with clearances and hence gear noise or insufficient preload of the pinion bearings, as the survey indicates the noise is worst when the bevel box is hot causing differential expansion between the aluminium housing and the pinion shaft. Not knowing the dimensions of the bevel box but If the bevel box is running at 120 deg C the pinion bearings are 50mm apart then the differential expansion cold to hot could be 0.06mm (0.0024 inches) which could be enough to upset the preload.