I'd lay the blame on Unreal here. It's possible to bundle the mono runtime with your game, it's just that Unreal has done it in a way that doesn't satisfy the LGPL. As long as the runtime is a separate binary for which all source is available, you're fine. This can be made completely invisible to the end user.
Maybe there's some difficulty I'm not seeing here, though.
To redistribute code written with Mono for Unreal Engine, you must have a commercial license to the Mono runtime.
These licenses are included in Xamarin's commercial products for targeting Mac, Android and iOS.
Xamarin product pricing starts at $0 for Starter Edition and adds Visual Studio support at $999 per developer, per platform.
In addition, you still need to comply to your license agreement with EpicGames for Unreal Engine.