Help with Big Sur and Broadcom Bluetooth Dongle?

I have an IOGear GBU521 USB Bluetooth Dongle.

It shows up in System Report as: BCM920702 Bluetooth 4.0

EDIT: I've found the solution, thanks to a little more googling and the good folks at Acidanthera. I'm leaving this post up, though, in case anybody has the same dongle and is having trouble.

According to the long details on this page, Big Sur users need to use BlueToolFixup.kext instead of BrcmBluetoothInjector.kext. So I removed the unnecessary AirportBrcmFixup.kext, kept BrcmFirmwareData.kext and BrcmPatchRAM3, and swapped in BlueToolFixup instead of BrcmBluetoothInjector, did a Clean Snapshot in ProperTree, and now everything's working great.

(The rest of my original post is below)

It used to work fine in Monterey but I guess Big Sur broke something with Broadcom bluetooth stuff.

I've been trying to follow the Broadcom WiFi and Bluetooth Kext instructions from the Dortania Install Guide, but I'm not having any luck.

Do I need to install both the AirportBrcmFixup and BrcmPatchRAM kexts? Or is one for Wifi and the other for Bluetooth?

When I install just the BrcmPatchRAM kexts (BrcmBluetoothInjector, BrcmFirmwareData, BrcmPatchRAM3) and run an OC Clean Snapshot, the computer hangs at boot. It continually shows an error saying it's refusing a core dump, and refers specifically to my BCM920702 Bluetooth 4.0.

If I also install the AirportBrcmFixup.kext and do a Clean Snapshot then it boots OK, but still won't allow me to turn on bluetooth.

I have a suspicion that it's an error in the loading order for my kexts. If I don't use AirportBrcmFixup.kext, Propertree puts the three Brcm* kexts in order at the top. If I do include AirportBrcmFixup, propertree puts just BrcmBluetoothInjector and BrcmFirmwareData at the top, AirportBrcmFixup later in the list, and seems to leave out BrcmPatchRAM3 entirely.

It just seems odd to me that ProperTree puts the three Brcm* kexts above Lilu. That can't be right, can it?