The ANA tickets are award tickets, I take it? If they're free tickets, then you won't collect any miles for the flights...

Is it possible to get free tickets from CLE from ANA using their code-share on United flights? This is the first thing I would ask...

In any case, I would book all your flights, domestic and international, through ANA, preferably as code-shares on the United flights. First choice, if they can do it: put them on the same PNR; then you're totally covered for a misconnect. Otherwise, have them put a notation on your PNR about the connections.

If you're worried about a misconnect (and I can relate to worrying about this), give yourself as much time as you can. Flights from CLE to IAD and ORD should be more frequent than flights to LAX (and much shorter), so I'd do my connections there.

David