Before you go further, consider replacing those screws. Since the gears turn freely, removing the old grease can be done tooth at a time with a tool shaped like a dental pick.
I once started to disassemble a Singer 128, because I didn't know how to free it up. I realized I would never get it reassembled, and passed it on. Turns out, it needed much less intervention than I realized. Also, taking things apart often leads to unintended consequences with timing.