OP:
I'm going to recommend
a completely different course of action for you.
I don't normally suggest that a user install a version of the OS using "a hack", but in this case, it may actually help. (see my personal experience at the end of this reply)
Do this on the MacBook with the working SD card slot.
I recommend that you visit dosdude1's page here:
When you get there, go to "My Software" and choose the Mac OS Mojave Patcher:
Just click the download and it will download an app "Mojave Patcher" to your drive.
Hmmm... here's the link:
It looks like this will work on a 2011 iMac without problems.
See if you can run the Mojave Patcher app on the MacBook.
Does it launch and run?
OK, then go to the "Tools" menu and download a copy of the Mojave installer to your MacBook drive, also.
Once it's downloaded, I believe the Patcher will ask if you want to create a bootable installer drive.
You DO, so insert your SD card and "point the way".
SD card shoud be pre-formatted to "Mac OS extended, journaling enabled, GUID partition format" (using disk utility).
The patcher app will take some time, but it should create a bootable OS on the SD card along with the patching stuff.
Take this to the iMac and see if it will boot.
Does it?
At this point, you can attempt an install.
Have dosdude's instructions loaded on the MacBook as you work on the iMac.
If you try this, let us know how it goes.
Personal experience:
I made several tries with High Sierra to create an installer drive and get it to boot my 2010 MacBook Pro (which can run HS).
Although I could get the flashdrives "completed", I COULD NOT get them to boot successfully -- kept getting errors that the installer was damaged.
As an earlier poster mentioned in this thread, it's a problem with HS. There are fixes, but they look like they can get complicated.
But... The Mojave patched installer drive on the SD card booted up, and looked like it could install Mojave on the MBP without problems. I DID NOT attempt an actual install, because I want the 2010 MBP to keep running an older version of the OS.
However, this won't be important to you. You just need to get that iMac up and running.
Good luck.