Thank you for providing the information. It certainly helps in trying to replicate what you are experiencing. First, let me say that you really shouldn't have to download software from the Epson site. The latest drivers would normally be pushed by Apple's Software Update.
If you specifically want the Epson Scan software, then you would have to get that from Epson. I personally do prefer the Epson Scan software over the standard Image Capture software, but that is only my opinion.
ILn any event, I followed your directions. I downloaded two files. The main printer drivers was a file epson14341.dmg and the Epson Scan software was epson14339.dmg. I did get two prompts. The first was to say I wanted to open the software downloaded from the web. The second was a standard authentication for the installer. Screen shots below.


Are you getting a chance to enter your username and password? Can you post a screen shot of what is preventing you from installing the software?