There's a product I often use to seal leaks, it works well and could be applied with a roller, but normally done with a brush.
It's called Acrypol Plus, comes in various sized tins and is like a thick paint that you apply liberally to leaks.
This said, however, will only be a temporary fix, will look awful and I doubt will be easy to remove from the glazing beads if your future plan is to replace just the ploycarbonate sheet. Clear silicone sealant down the joints would be the better option if you can reach them and they are totally dry beforehand. It may be possible to slide a couple of panels out from the eaves to allow you to place a ladder up from the inside and work through the gaps.