Theoretically that DOT rule is very nice. However, keep in mind that the "Avianca" UIO-GPS flight is operated by "Avianca Ecuador" aka Aerogal. Aerogal does not have any presence in the US and is therefore not expected to know about US law and is certainly out of reach of US authorities. So the Aerogal check-in agent can certainly tell the OP to pay up, without any fear of repercussions from the US DOT. Their country, their rules. If OP were charged, what would he/she do? Complain to US DOT after the fact? Good luck getting DOT to enforce anything against an airline that does not have US nexus.

Also, I note that Aerogal/Avianca offers two classes service on the UIO-GPS route. Economy gets one free bag (second at $30), business gets 2 free bags. OP says is traveling in business, and if that is the case then no worries, two free bags even if they apply their own rules. But is OP booked perhaps in economy on the UIO-GPS segment? In that case, if they apply domestic economy baggage rules, the charge for the second bag would be $30. So I would not worry about getting charged $150 at any point. They either apply US rules which would be $0, or local Ecuadorian rules which would be $30.