I might give this a try! Out of curiosity, do you have a 13" or 15" 2011? I have a 15" and might give this a try from High Sierra to Monterey but I'm concerned as my GPU died and I'm using a NVRAM workaround to disable the dGPU. Has this happened to you?You can create a bootable USB Monterey Installer using OCLP Patcher. You can then use the USB stick to update to Monterey.
I did that for my 2011 MBP (from Catalina to Monterey).