I've never used Garmin Express to manage the maps on my devices, so I don't know it works.
Is it trying to send the maps to the internal memory rather than the SD card?
Do you have any control of where it sends the maps?
Can't you just browse into the device from Windows Explorer, and have a look at what's using up the space?
The Edge device will appear as 2 drives in Windows Explorer: the device itself ( very small storage space ), and the SD card ( where the maps need to go ).
The maps should be a several GB file on the SD card:
<Drive-letter of SD card>\Garmin\gmapsupp.img
Try moving the old map file over onto your PC to free up some space, and then trying the map update.
Otherwise, I'd just install the maps manually, but I'm not sure how you are sourcing your maps so I can't say more.