[Editor Plugin] Grabbing thumbnails?

I have a project which requires the thumbnail textures of various static meshes (there are more than 300 of them).
After experimenting with various runtime methods of doing this dynamically, I finally decided the best route is probably to create an editor plugin which utilizes FAssetRegistryModule to listen for whenever an FAssetData entry has been added. I have done this successfully, like so:

UMyAssetManager::UMyAssetManager()
{
	TargetPath = TEXT("/Meshes/");
	FAssetRegistryModule& AssetRegistryModule = FModuleManager::LoadModuleChecked<FAssetRegistryModule>("AssetRegistry");
	AssetRegistryModule.Get().OnAssetAdded().AddUObject(this, &UMyAssetManager::OnAssetAdded);
}

UMyAssetManager::~UMyAssetManager()
{
	FAssetRegistryModule& AssetRegistryModule = FModuleManager::LoadModuleChecked<FAssetRegistryModule>("AssetRegistry");
	AssetRegistryModule.Get().OnAssetAdded().RemoveAll(this);
}

void UMyAssetManager::OnAssetAdded(const FAssetData& AssetData)
{
	auto assetName = AssetData.GetFullName();
	auto assetClass = AssetData.AssetClass;
	if (assetName.Contains(TargetPath) && assetClass.IsEqual(TEXT("StaticMesh")))
	{
		auto assetRef = AssetData.ToStringReference();
		// Do something with this asset reference here...
		// ...(for example, load & cache it into an array, like below)
		FStreamableManager AssetLoader;
		auto Asset = AssetLoader.SynchronousLoad(assetRef);
		if (Asset && Asset->IsValidLowLevel()) {
			Meshes.AddUnique(CastChecked<UStaticMesh>(Asset));
		}
	}
}

So now that, with the code above, we can know when each individual mesh is added to the content browser, all I need is a way to access the FAssetData's thumbnails. Does anybody know how this can be achieved?