Even though you can handle all feedback from within Feedbucket, that is not the intention of the system. Instead you should continue to use the project management tool that you are using today but let Feedbucket automatically create tasks in there with screenshot or videos attached.
Allow your team to only work inside of your project management tool when communicating with the reporter. The integration will notifiy the reporter when a team member comments inside of the project management tool. This way your team does not have to log in to Feedbucket at all! Everything like it is right now but better.
Lots of integrations has already been created. Do we not have an integration for your project management tool? Please let us know because we are constantly adding more integrations.