Thanks for the reply! I tried this method and, while it didn't work perfectly, I did ultimately manage to retrieve my photos and videos.
I followed the instructions, including the detailed updates, and restored (without taking out the SIM card) at night. Things were progressing well when I went to bed, but when I woke up in the morning and checked the phone I noticed that the previously counted and then still increasing ~1200 of 2100 photos that I'd had on the phone were mysteriously reduced to only 4. I thought that for whatever reason the connection had dropped and the transfer had failed during the night, and so I was prepared to erase the phone and then start over again. Thankfully before doing so I checked the storage allocation bar for the phone in iTunes and there I saw that, while the phone itself was showing that I had only 4 images saved, the phone actually had about 9 GB of photos on it. As I wasn't sure how to retrieve them from the phone, even though they were there, I searched for a solution online. What I found among the search results was a recommendation of downloading and using the program iExplorer, which I did and which was able to show me at least a listing of the image files that I had been missing and a set of previews of some of them. Following the recommendation's instruction, I deleted two list-type files from the phone through iExplorer, in the hope that when I later restarted the phone the photo Gallery would be forced to rebuild the index of all the images on the phone and thus show me all my images. While reportedly this technique had worked for some people, for me it definitely did not; after being restarted post the files' deletion, neither the phone nor the storage allocation bar showed me that there were more than 4 photos in memory. Fortunately, however, I had done a back-up of the phone on my computer before deleting the files. While at that moment I had planned on simply restoring from that backup and then trying through iTunes to transfer the hidden 2100 photos to my computer (an action that iTunes seemingly at the time would allow but that I later learned would also most likely not have worked for me), I ended up restoring from a "new" backup that, I'm sure, hadn't been there previously. This "new" back-up was dated the same day as the iCloud back-up from which I had tried to restore the phone the previous night. Curious, I chose to use this back-up, instead of the back-up dated earlier that morning, which I thought would have everything including the hidden photos (but which later I found out did not). It seems that sometime in the restore from iCloud the photos that I had been hoping to recover finished downloading and then were saved in an asynchronized part of the phone, where they couldn't be successfully retrieved at the phone level because of the mismatch in date. After I restored from the "correct date," which really didn't exist before the back-up to my computer that morning, the phone successfully showed me all the photos and videos that I had been missing (but could not successfully show me apps or other backed-up data). I then was able to recover simply through iPhoto all the photos and videos to my computer. Hoping that everything could be synchronized in one final attempt at restoring from iCloud, I then erased the phone and started one last attempt at restoring from iCloud by again following all the instructions above. Unfortunately, the transfer this time failed to port over any of the photos at all, but caring less about their being on the phone now that I'd safely recovered them to my hard drive I prioritized having my apps and other backed-up data on the phone, chose not to try restoring from iCloud anymore, and left the phone as it had restored then. So, while this method didn't entirely successfully restore my photos and videos, it still ulitmately helped me recover them. Hopefully this information will help anyone else facing similar issues in recovering photos and videos from iCloud - an action that, with how much Apple vaunts the ability to do so, should definitely be refined soon.
In the meantime, I've just noticed that after updating my OS (including iPhoto and Aperture) to the newest version this week some of the photos that are actually within the joint Library folder on my hard drive aren't showing up anymore in my visible Library in iPhoto - and that my Aperture won't even open anymore without crashing. I'm wondering if these errors may be related to the difficulty with my phone, but I'm generally looking for a solution now to this issue (in case anyone reading may know of one).
