OP:
"I did that, but it appears that if you have a completely dead internal drive it just won't work properly off an external drive. I can get it to boot and it can run some programs, but can't mount any hard drives or use any additional external hardware."
This is completely erroneous.
I've been booting/running all kinds of Macs (since my first Mac SE) since 1987 using external drives, both platter-based and SSDs.
Once booted, the Macs are completely functional (as if booted from an internal drive).
Before I bought this 2018 Mini (which also can boot fine from external drives), I booted and ran my 2012 Mini for SIX YEARS from an external SSD, its entire "working life". No problems.
Good to see that you got the iMac working with a replacement internal drive, but something wasn't right when you were booting from an external drive...
"I did that, but it appears that if you have a completely dead internal drive it just won't work properly off an external drive. I can get it to boot and it can run some programs, but can't mount any hard drives or use any additional external hardware."
This is completely erroneous.
I've been booting/running all kinds of Macs (since my first Mac SE) since 1987 using external drives, both platter-based and SSDs.
Once booted, the Macs are completely functional (as if booted from an internal drive).
Before I bought this 2018 Mini (which also can boot fine from external drives), I booted and ran my 2012 Mini for SIX YEARS from an external SSD, its entire "working life". No problems.
Good to see that you got the iMac working with a replacement internal drive, but something wasn't right when you were booting from an external drive...