I have to preface this recommendation by saying that 1) I haven’t used this software, and 2)I don’t know for sure that it does all the things you need.
That being said, the buzz about Advokit among some in the grassroots activism community is that it has a lot of potential. I’ve actually been meaning to play with it, but it’s down on my list a ways. It’s created to manage voter and volunteer lists for campaigns, but I don’t see why you couldn’t use it for an organization.
You can create different users with different rights and access. Check it out.
The thing is that something as ambitious as putting your importing your entire membership database or installing a script like this will probably require you to either increase your knowledge on web stuff or find one of your members or a volunteer that can help with the heavy lifting while you work out the bugs.