First point: that belt seem to be sitting rather deep in the pulleys. aussie, you said it is a new belt: are you sure it is the right section size (i.e., width of belt)? And is it the right length, so the tensioning device is well within its movement range? If the belt is bottoming in the drive or driven pulley, or if the belt tension is less than it should be, you will get approximately the problem you are having.
With regard to the clutches, I've had clutches slip at full clamping force if they had oil on them. Your current problem could be due to having oil on the friction material of the forward clutch, but not the reverse clutch. However if one of them were that oily I think you'd see it: oil would be thrown out of it when it was running, and would make a mess around the clutch. I see no sign of that near your clutches. The other reasons for clutches to slip are insufficient clamping pressure, too much torque to transmit, or too much heat due to having run too long in a slipping condition. (In my foolish youth I learned that if you speed-shifted a Holden 202 cubic inch 6 (red motor) with a four speed manual transmission from a standing start, by the third acceleration run the clutch took a while to bite when you shifted into third and fourth. The clutch was hot by then.) Considering those possibilities in sequence, lack of clamping pressure is quite likely if your clutch disk is, for example, seized onto the central shaft. Your clutch could only be overloaded by too much torque if your rear axle or chain drive had seized up, and if that happened it would probably affect reverse as well as forward movement. Your clutch is slipping even from a cold start, so I don't think it is an overheating problem.
That seems to point to two things worth looking at. First, with the engine not running and the clutch pedal not pushed, is your mower easy to push both forward and backward? If so, it probably isn't a jammed drive train. Second, when you push the pedal forward and backward, does it have the same amount of reserve travel in both directions, or does it come much closer to the end of its movement in the forward direction? Is the friction material of the forward clutch the same thickness as for the reverse clutch?
