FYI for anyone who comes across this same problem.
I’ve had exactly the same problem and am using Dreamhost. Firstly, I don’t think it’s to do with the plugin, but rather the limited memory space we get on shared Dreamhost accounts. There are two things you can do:
1. Optimise your WP database. I think it gets unstuck when you are importing a large SQL file. So I suggest using something like WP-Optimize to shrink your database file. This worked first go:
http://ww.wp.xz.cn/extend/plugins/wp-optimize/
2. Change your DH domain settings and untick FastCGI and extra web security. This apparently eats up memory resource so disable it for you to run the duplicator install script.
https://discussion.dreamhost.com/thread-131416-post-142854.html#pid142854
Hope this works for you.