I wanted to report positive results after attempting the Big Sur
11.2 upgrade on a 2011 21.5 iMac. I used option #7 from the first page.
MicropatcherAutomator - this is another frontend using the micropatcher backend. The GUI makes it more comfortable to create the USB installer and follow the installation and patch process. It supports macOS 10.11 and later to create a bootable installer - so it closes a gap for a users starting with systems having older macOS versions currently installed (option 5 starts with Catalina, only).
I have been able to install Big Sur on a 2011 iMac. This machine has been upgraded with an Nvidia K1100m GPU card and the Broadcom bcm94360cd BT 4.0 & WiFi upgrade.
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The patcher worked very well with the user-friendly interface and simple instructions. At the place and time where the computer is installing Big Sur, it goes into another boot screen that I can not see as my GPU upgrade has caused me to lose a portion of the boot/loading screen. So after about 1 hour of watching the black screen and hearing the computer still running, and assuming it had finished. I simply turned it off with the back power button. Held Option key while restarting and booted from the Big Sur partition.
Voilà! Big Sur loads up and asks for all the usual basic settings, like country, language, etc. Loaded up well and then but still needed a few patches apparently as the sound was initially unadjustable for example. Rebooted and ran the suggested patcher program and now all appears to almost be probably as good as it can get.
Drawbacks and changes I have noticed overall with the hardware GPU and OS upgrade are:
Must use Mac Fan Control permanently as my fans will run full speed because the GPU temprature sensor somehow does not work with the K1100m upgrade.
Screen brightness is unadjustable (but not much of an issue)
Sleep mode does not work the way it used to, have to turn on and off without use of sleep mode.
??Fixable??
A second monitor hooked up through the Thunderbolt 1 to D.P. connection works in High Sierra but not Big Sur.
Apple TV movie library does not want to play or download
Other than that all normal computer processes seem to be working perfectly. The App store was usable, Final Cut Pro after limited testing seems to work perfectly as well as Microsoft Word and Excel.
Thank you all who have worked to help make this possible.