Anna_webbins thank you for the great question.
Integration (between different applications, sites, etc.) was always scary and also a complicated task; and one of the biggest problems is resource identification. For example, if you have Website A, that has the page "Hello World" and Website B also has the page "Hello World", it does not necessarily mean that this should be treated as the same things. Most likely they will have even different IDs.
Your problem is not unique. There were many people in the past asking me similar questions. The normal Import/Export functionality does not satisfy the ongoing needs of website administrators. That is why at the beginning of 2019 I've introduced the concept of Access Policies that allows you to define JSON-based policy that can be applied to any role, individual user or all users at once. This eliminates the need for a website administrator to use AAM UI to define access settings, which can be quite tedious if there is a need to do that on multiple separate sites.
As of May 2019, I'm almost satisfied with the stability and performance of the Access Policy concept and already considering vendors for the next phase, which is the distribution of those policies across multiple sites.
As of now, you can convert all your AAM settings to Access Policies and transfer them between your 2 sites manually.
Keep me updated if anything.