The problem with a top-on repair is that the bar is sprung. It can be done, but you really don’t want to.
Just pull the top. Use the bar’s spring to push the top back into round and, as James suggests, apply fabric patches soaked in hide glue over the ends of the bar.
I’ve done it with 4” squares of old denim.
When it’s time to put the top back on, don’t bother trying to get it all done at once. Glue it down to the neck and bottom blocks, then the corners, finally the rest of the ribs. Use very thin glue for this part.
Just pull the top. Use the bar’s spring to push the top back into round and, as James suggests, apply fabric patches soaked in hide glue over the ends of the bar.
I’ve done it with 4” squares of old denim.
When it’s time to put the top back on, don’t bother trying to get it all done at once. Glue it down to the neck and bottom blocks, then the corners, finally the rest of the ribs. Use very thin glue for this part.