As Matt advises, using a correct, specific movement holder for the movement will help as it has a support for the seconds wheel..
DSC05591.JPG by Micky Aldridge, on Flickr
Yup, you will need to replace the bridge plate, and transfer the gears across. Alternatively, replace the complete bridge with another with gears if you don't think you would manage to transfer the gears yourself.
I have a special broken screw extractor which would get that screw on in no time, its something I use often, but irrelevant to a non-watch repairer.
Looks gen, if there is a rep like that then Im getting one lol
Is this you?
https://www.facebook.com/photo.php?fbid=1051285504951627&set=gm.1739178186351885&type=3&theater