How do I customize the details panel of the Static Mesh editor?

I am currently working on customizing the details panel for the Static Mesh editor with the aim to trigger some functionality (currently only logging) when pressing a button in Unreal Engine 4.27. But editing this particular details panel is proving to be more difficult than expected.

I was able to successfully add the button to the StaticMeshActor details panel using either category “Materials” or “StaticMesh” as can be seen in the image and code below.

void FMeshHoleFixerModule::StartupModule()
{
	// Register details customization
	{
		FPropertyEditorModule& PropertyModule = FModuleManager::LoadModuleChecked<FPropertyEditorModule>("PropertyEditor");
		PropertyModule.RegisterCustomClassLayout("StaticMeshActor", FOnGetDetailCustomizationInstance::CreateStatic(&FStaticMeshDetailsCustomization::MakeInstance));
		PropertyModule.NotifyCustomizationModuleChanged();
	}
}
TSharedRef<IDetailCustomization> FStaticMeshDetailsCustomization::MakeInstance()
{
	return MakeShareable(new FStaticMeshDetailsCustomization);
}

void FStaticMeshDetailsCustomization::CustomizeDetails(IDetailLayoutBuilder& DetailBuilder)
{
	IDetailCategoryBuilder& CategoryBuilder = DetailBuilder.EditCategory("Materials");

	CategoryBuilder.AddCustomRow(FText::FromString("My Button"))
	.ValueContent()
	[
		SNew(SButton)
		.Text(FText::FromString("Click Me"))
		.OnClicked(this, &FStaticMeshDetailsCustomization::OnMyButtonClick)
	];
}

FReply FStaticMeshDetailsCustomization::OnMyButtonClick()
{
	UE_LOG(LogTemp, Warning, TEXT("Button Clicked!"));
	return FReply::Handled();
}

I have however been unable to add this button to any of the categories of the Static Mesh editor details panel. I can’t find any documentation suggesting which ClassName to pass into RegisterCustomClassLayout or which CategoryName to pass into EditCategory.

Has anyone done this before and know how this can be achieved?

Preferably, I want the button to be added to the various LOD categories (i.e. LOD 0, LOD 1 etc.) just below Reduction Settings.