Also, I like the whole idea that if there is a safer place withing the person's country to go to they should go there first. Whether we can talk about countries they pass through is a good question and I'd ask Albaby.

Not without amending the statute. Trump tried it. His efforts were struck down by the courts in 2019 (an injunction was imposed literally eight days after the rule was promulgated). Below is the link to the circuit court opinion upholding the lower court injunction, and the relevant quote that deals with this issue:

"Similarly, the safe-third-country bar under § 1158(a)(2)(A) allows the United States to deny asylum on the ground that the alien may be removed to and apply for asylum in a safe third country. But entirely absent from the Rule are the requirements under § 1158(a)(2)(A) that there be a formal agreement between the United States and the third country, and that there be a “full and fair” procedure for applying for asylum in that country."

cdn.ca9.uscourts.gov: PDF document

TL;DR - the statute requires a formal agreement in order for the safe third-country exception to apply, so unless the U.S. has a formal agreement with a safe third-country (which we don't with any of the relevant central american countries), the Executive cannot impose that requirement administratively.