Anthony,
when you say that the belts are slipping, do you mean that both belts are slipping on startup or that there is differential creep between the two belts. If the latter, it is not really a problem as there is bound to be some differences between the two belts and even the pulley grooves due to manufacturing tolerances.
When you are starting in higher speeds, more torque is needed, just the same as trying to start your car moving in top gear, so what ever else the problems you have I wouldn’t over tighten the belts apart from anything else excessive bearing wear can be caused.
We used multi belt drives on large chain conveyor systems and there would always be some differential creep between some of the belts and they had to move large loads of loading when starting and the initial inertia was huge and they would be constantly stopping and starting during production runs,
Actually belt drives aren’t quite as simple as they seem. Only one side of the belt does any work at any one time. It is the portion ot the belt that is being pulled by the driver pulley from the driven pulley that is in tension and does the transmission of power. The other portion of the belt from the driven to the driver is doing very little. As the belt passes round the driver back to the driven, the driver is effectively pushing the belt and there is comparatively little tension in it. As the driver pulls the belt from the driven, the belt is pulled deeper into the vee of both pulleys and the friction is what transmits the effort, the other side of the belt can flap about quite a lot. In my early days of driving when the ‘fan’ belt slipped it was quite common to apply rosin powder, (same as used by violinists on their bows) to increase the friction and grip of the belt rather than over tightening because it was too easy to wear out the bearings of the water pump and dynamo given such a long belt and the excessive tension needed to tighten it. That was a short term fix until a new belt could be bfitted.
Terry