ANA tool is more accurate than united.com when it comes to LH F availability. As smichelm said, however, LH doesn't release F award until ~2 weeks before departure. The good news is that this is pretty consistent. So I'd suggest to book decent flights available right now and look for LH F later (no change fee for 1K/Plat).
If you don't mind connecting in Canada, AC out of YYZ or YVR may be an option. Their biz product is quite good too.