Hello Dafni,
Finding ways to automate the process of locating and retrieving full text documents will always present challenges. It usually involves two steps: identifying where the document can be obtained and then finding a way to retrieve it.
The Find option in EPPI-Reviewer addresses the first step. It will generate a search based on title and author and run it in Google. We use Google because it will search everywhere possible including Google scholar. If the item is accessible to Google's trawling it will find it. Although there isn't a way to change the search engine the 'Find' function uses you could cut and paste the Google search into other search tools such as Bing.
Addressing the second step, retrieval, can be a bigger problem. Reviewers will have varying levels of access to different journals depending on the access their home institution provides. We are lucky that being based at UCL in London we have access to a large number of the world's journals. Many reviewers will not have that level of access so trying to automate this process would be very difficult as we wouldn't know the level of access each reviewer has.
To further complicate the issue, you might have access to a particular journal but the item you require might not be available in electronic format. You would still be required to order a copy of it (or photo copy it)
Taking all of this into consideration it means that creating a 'one-click' system for retrieval would be very difficult. I understand that EndNote tries to do something like this but as you mention it doesn't always work very well and any time it may save you could be lost sorting out it's 'almost found' items. We still do most of our retrieval on an item-by-item basis as we haven't found a system that works better (yet). If you want to try EndNote you could export your 'includes' from EPPI-Reviewer and import them into EndNote.
You could also look at Mendeley to help with full text retrieval. I'm not familiar with it but I understand it tries to do something similar to EndNote.
Best regards,
Jeff