How about a different seat?
I am not familiar with your dinghy, but I assume that the straps the broke are the wooden seat slips onto. If that is not true, disregard the remainder of this suggestion.
Instead of trying to fix the existing seat and straps, buy an inflatable seat that will fit between your side tubes. Glue Velcro pads to the end of the seat and to the spot on the side tube where the seat should be located. Then just inflate the seat to hold it in place.
