I haven’t tried Peru, but LATAM Brasil won’t work at all on the Brazilian site if you’re using a non-Brazilian card or don’t have a Brazilian address/CPF. The LATAM US site SOMETIMES works, although fares are always either a little higher there, or sometimes multiples higher. I will clarify that this happens to me even though I’m physically in Brasil. The problem is not having a Brazilian bank card and CPF/Address.
Another tip, don’t try too many times before calling… each time you go through the process and get to the payment page, a temporary reservation is made (they don’t give you the locator number though…) and you can easily end up forcing yourself into a higher fare category when you do call as you’re already blocking inventory due to all the earlier attempts.
Sometimes I really wonder how LATAM manages to sell to anyone. For many years their system of receiving money from us has been a complete shambles.