Good news and maybe some bad news.

Should not be a problem transiting LAX btwn SA and Europe. I have done it the other way several times. LA600 should be one segment but...

LA600 doesn't offer first btwn EZE and SCL but does SCL-LAX. If LA forces this to be two segments then you are over the limit in SA. This is a strange situation. I'd suggest ticketing EZE-LAX open in first and then let LA downgrade you to business out of EZE. Maybe they'll let you sit up front anyway.