I can not recommend which border, but I can recommend a process. Plan your stop the day before at a US border town, and make time that day to visit the Mexico border crossing, and take care of all the paperwork. Then return to the US to spend the night.
The next day, cross first thing in the morning with no stops, and you will be hundreds of miles south of the "troubled area" before you need to stop for the day. In January my wife and I will be crossing at McAlllen/Reynosa and will be out of the state of Nuevo Leo mid afternoon, before we stop.
FYI - my understanding is that most of the extended health policies in Canada will not cover you in the Northern Mexico states where a "Travel Warning is listed by the Canadian Government". We will travel through and be out of that area the first day.