The ArcadeVGA 3000 will probably do what you want.
I assume you have J-PAC because of the doubled image. If that's the case, then you should just be able to plug the J-PAC into the new computer and all your joysticks and buttons will work exactly as before. No configuration from a hardware perspective is necessary. You'll probably need to do some configuration for a few games in MAME where the default buttons aren't set up how you'd like. But this config is done entirely from within MAME.