Thanks for subscribing.. hopefully you're issues above haven't cropped up, but I'll answer what I can here.
First off, we haven't used the Share Me Compact Pro, so I don't know which Facebook library they're using along with possible incompatibilities. We use the 'new' one, so if they do as well, even if there are minor issues, we should be able to help you overcome them. Just let us know. However, we have a Like module in JFBConnect as well as 'tags' which you can add to any article individually or to your template to add them to your whole site. By simplying typing { JFBCLike}, a like button will appear. There are other configuration options you can use in the tag for showing faces and such, but that's how easy it is to do.
As for your stats, you can definitely keep them, but it may take some effort. Basically, for each Like button, you (or your extension really) has to tell Facebook a unique ID for that button. If you use our modules, you'll just need to make sure you configure them to use the same ID, per page, that the Share me module was doing. Again, we can help you understand how to do this, but we don't do it automatically.
Best of luck, and thanks again!