Air transit rules are getting worse year after year. For my wedding I had big time issues in bringing my parents (from India ) to Mexico. adding, if visa gets rejected from one embassy, it's a pain. I had 2 options -
India - USA - Mexico - this didn't work out coz us rejected tourist visa. I ended up booking the below option, because for any halts I needed to apply tourist visa /ETA for my parents, and takes 30-45 days per embassy ( which is far away from home )
India - Damian/Bahrain - São Paulo( Brazil ) - Mexico --> total travel time 40+ hours for parents ( who are in 60s and 70s. None of these countries need air transit visa if staying less than predefined amount of time for Indian nationals.
It was painful, until Amsterdam embassy emailed me I can do layover for less than 24 hours without visa. Ultimately the route I choose was India - Amsterdam - Mexico lol.
I understand the frustration of original poster, traveling is becoming more hassle year by year. Travel agencies may not be able to help always, especially if it's not popular routes.