As far as i know, you'll need a copy of the Mitsubishi PLC Programming software. GX-Developer Version 8 is the most up to date. Im don't think there is any way to download from the EEPROM to your PC without the Mitsubishi software.
Once you have GX-Developer installed, Davefinic suggestion should work. Upload from the EEPROM, (save the code), remove the EEPROM, then when you download the code it should go straight to RAM. Like Davefinic i've never tried this.
Another thing to try is in the "Online" tab (at the top of the GX-Developer software), there are two options, one for 'Write to PLC' the other is 'Write to PLC(FLASH ROM)'. If your select 'Write to PLC' i think it will write to the RAM.
Hope this makes sense and helps