Restoring Saved Webpages on Home Screen from Backup

For a restore to work, the data must be backed up in the first place.

I managed to restore my information from a backup that was made a few months back, but one of the most important things that wasn't restored were a large number of Safari webpages saved to the home screen

The critical piece here is, was all that work you did backed up at any point? If the last backup was made "a few months back," you won't be able to restore anything since because it simply doesn't exist. From what you describe, it wasn't backed up.

Unfortunately, nobody is going to be able to assist as you've found with your latest interaction with Apple. You will have to re-create it from memory.