It should be trivial to split it up into 1GB chunks or whatever. In fact, if you only request single pages, you could split the database up into pagesize-sized files. This is a lot of files, but at least it avoids the need to do range requests at all. You probably want to increase the pagesize a bit though (e.g. maybe 256 KiB instead of the default 4 KiB?)
Range requests are the star, so I would vote keep them? I mean, technically, the CDN could represent each 4kb block of the file as an individual URL, so that you do range requests by filename instead of by .. range request .. but at some point I definitely think RRs are more sane.
Probably both, compute file name and relative offset from the original offset. (A minor complication is requests crossing file boundaries, in which case you have to do two requests instead of one.)
