Seems simple enough to just lower the box drain then?

Honestly this would be my move too. As far as I can tell from OPs comments, it's not really working or solving any problems now (please let me know if I missed something though, it doesn't sound like OP has water management issues even with that yard slope aside from this drain pipe clogging). Why go through a ton of work and potentially multiple fixes and digging up the yard to get this set up to continue to not really do much of anything? I'd pull the whole thing out and just let the grass move up to the edge of the sidewalk.