So, after some experimentation, I found the solution myself. Since all of the steps are covered elsewhere already, I’ll just go over them quickly:
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First, I installed the correct version of TWRP compatible with Android 12. For a step-by-step, go here.
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After that was done, I downloaded the latest images for LineageOS 19, LineageOS 18, and of course eOS, for my phone, and put them on an SD card that went into the phone.
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From TWRP and the SD card, it went like this: install LineageOS 19 with the instructions here.
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Reinstall TWRP
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Install LineageOS 18 with the above instructions.
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Reinstall TWRP
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Finally, install eOS with the same instructions.
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Reboot, and watch the e bounce happily up and down on my screen.
It was a bit of a trial run at first, getting TWRP on the phone the first time, but after I had that down, everything else went smoothly.
So hopefully this can help others with similar trouble. You don’t have to downgrade a Samsung phone to the Android version fit for your eOS via official firmware, you can simply install LineageOS over the official firmware on your phone, downgrade that very easily, and then switch to eOS.