You don't move the entire site to DreamObjects, only the large files. Keep your index files where they are, and update the links on them to reflect their new location in DO.
There are a number of apps that will let you get around the 64MB browser limitation. You can see a list of them here:
I use CrossFTP on Windows and Linux, where the free version works well. I have previously used Transmit (which is not free) on Mac; it is solid, well-supported, and I recommend it.