Can't Reinstall Monterey OS in Recovery Mode

I have a 2019 27" iMac running macOS 12.3.1. (Monterey). It has now crashed on me (for no apparent reason) for the second time. When I try to do a normal boot up, it just boots up to the international "Do Not Enter" icon with a web address for Apple support. 

I have tried to restore my OS by downloading a new copy of the Monterey OS from the web. This doesn't work very well where I live since my fastest download speed is around 22 mbs, so I have attempted to do this from my daughter's house who has cable internet speeds of 500 mbs. Still, every time it crashes.

So I have tried to create a boot installer for macOS following the instructions contained in an article that appeared in MacWorld on May 20, 2022 (https://www.macworld.com/article/671308/how-to-create-a-bootable-usb-macos-installer.html). I have created two different boot installers with the Monterey OS downloaded from the internet and installed on a flash drive (one a USB 3.0 and the other an older version of USB) using the createinstallmedia command via the Terminal program. The boot installer seems to be created through the Terminal program, but every time I try to use the boot installer to transfer the OS to my iMac's hard drive, it fails. As the article suggests, I have checked my boot up security and it does authorize booting from an external disk. I have attached a picture showing the Recovery Log from one of my many attempts.

I have taken my computer to the Apple store and they tell me I must wipe my hard drive and install a new OS. Unfortunately, this means losing everything I have accumulated digitally over 71 years of life (especially photos). Since in the rural area where I live there is no high speed internet, using the Cloud as a back up is not feasible and I long ago ran out out space on my Time Machine. Any suggestions you might have would be greatly appreciated. 

I am at a loss that the back up systems that Apple supplies (downloading a new OS from the internet or installing from an external boot disk) appear not to work.

Thanks.