Your best bet is still to talk to Apple. I would schedule an appointment with the "Genius Bar". Talk to someone other than the person you talked to before. That person is likely telling you the truth...that there is nothing you can do, but it might be good to be on the safe side and talk to someone else at the Apple Store or call into the toll-free number (if it is a new phone, you should be eligible for free support through the toll-free number).
If the only place that you have those pictures is in iCloud, then you are at the mercy of Apple. While in theory they likely have backups of the data on their server(s) that might go back some period of time and could in theory potentially restore that data, they are likely not willing to do so. They will likely point out some clause in their iCloud agreement that essentially says you store your data with them at your own risk. But, it does not hurt to try.
If you put the pictures some where else (either through direct actions of your own or indirectly by way of iCloud functions), then there might be ways for you to recover them. Do you use iCloud with a computer (Mac or Windows PC)? If so, then your photos might be on that computer.
For a Mac, you would need to have iCloud setup in the System Prefs and Photo Stream (best chance) and/or iCloud Library (still might work) turned on in those settings. If you have Photo Stream active, then your photos should be in the Photos app (or iPhoto if an older version of the Mac OS). If you only have iCloud Library setup, then I honestly don't know if it keeps a local copy on your computer or completely relies on cloud storage. If it is the former, them you might still have those photos on the computer. If it is the latter, then you are out of luck most likely.
For a Windows PC, you would need to have the iCloud control panel downloaded, installed, and be logged into iCloud...and have Photo Stream and/or iCloud Library active. I am less familiar with using iCloud on Windows. This link should help with iCloud Library:https://support.apple.com/en-us/HT205323
This link will give more info on Photo Stream, but on a Windows PC, it will download any photos added to the Photo Stream to the designated folder:https://support.apple.com/en-us/HT201317
If you don't have iCloud setup with a computer, then you are likely out of luck. Your only other chance would be if you have another iOS devices, but if everything is cloud based, then you might be out of luck even there.
For the future, I would suggest you manually copy/backup your photos to some other service in addition to iCloud (a good option is DropBox as you can install the DropBox app and set it up to automatically upload all photos from your camera roll to your Dropbox account...just make sure you have enough data allowable on your DropBox account) or to a computer that you own. I generally recommend to NOT rely on just a single cloud service to backup anything. If you do, you are completely at their mercy. And personally, I backup my iOS devices to my computer rather than iCloud, but that is my just my preference.