Honest opinion here - but if you are "seeking asylum" then crossing 5 countries to the one of your choosing isn't asylum.
Asylum is going to the nearest safe place to rid yourself of domestic-based dangers - of which there are plenty of reasonably safe ones throughout South America - and likely plenty within that same country.
Ignorance is not an excuse. If you want to immigrate legally, be honest. Claiming asylum and crossing 5 borders is fucking hilariously stupid. You're asinine if you call that asylum.
People from Guatemala cross 1 border before appearing at our own. People from Honduras & El Salvador cross the Guatemalan border twice to get here. Mexico has to let them thru to maintain domestic tranquillity.