A few things which you may find interesting:
1) Google Play will allow you to upload up to 1000 of your own books. You can then read in the web based reader. The format is epub but I'm not sure if it's epub3 compatible.
2) I used to have an ereader app on my ownCloud installation. It meant I could open epubs in the browser. It worked but it wasn't the greatest experience. Since then I've moved to Nextcloud and not bothered to re-install the app but I notice it's still available and there are others. (do a search on apps.owncloud.com). Even if you didn't want to go to the trouble of setting up your own ownCloud/Nextcloud you can always look at the source.
3) I also used to use a Chrome extension that was an epub reader. It actually downloaded the files and cached them somewhere but it was not bad. I think it was
this one - which seems to be unavailable now. Might be worth trying to contact the author.
4) From what I understand Calibre 3.0 will have a server with a built in web reader. However, I seem to recall Kovid's not a fan of epub3.
Finally just to echo meeera's point, using the current calibre-server I can download my books remotely easily enough, even directly into an app if it supports OPDS.
HTH
EDIT: I posted the above before I saw your reply to meeera.