You have tried absolutely everything I would suggest normally for iPhone setup issues.
I remember and issue ‘like’ this one with someone else phone (one that I had access locally), and the solution in that case was to completely remove the dreamhost account from the iPhone and readd, but you’ve already done that. (that issue was also pre-iOS 8)
I have a couple dreamhost mail accounts added on my iPhone and didn’t have problems with iOS 8 (or 8.0.1 or 8.0.2) and my dreamhosts accounts.
iOS 8.1 is scheduled for release tomorrow (Monday). I just read a condensed change log for the release and saw a couple of items that I wonder if will help your case. You might check for updates manually to get it sooner, otherwise you should get the notification to update in the next few days. AFTER the update check again of course, and I think you may have to delete the account entirely from you phone again and re-add it after the update.
Also possibly relevant, what model iPhone? (since you updated to 8, that says it’s not a iPhone 6, one of the items in the change log will only effect iPhone6 users, but appears relevant)
Also possibly relevant, is the same appleId used for iCloud sign in on this iPhone also used by ANY other iDevice for iCloud signin? If so, is the mail switch in the iCloud screen on or off? If so, do you have the same problem on the other device or is it working?