needle jamming down on Singer 8280 - can I fix timing?

I was sewing through several heavy layers of fabric with my Singer 8280 sewing machine, and suddenly the needle jammed in the 'down' position and wouldn't come back up.

I have tried everything I can think of, but every time the needle goes through the fabric to the bobbin, it clunks and gets trapped down there and won't come back up until I unscrew the pin and and remove the needle from the machine.

I assume it's the timing that's gone - is there a way I can fix this myself?