Qualitas.
I keep in mind that liability serious injury claims are the deciding factor. If the other party has someone seriously injured the cops take you to jail. Most of the time they'll not lock you in a cell but allow telephone calls to get things arranged.
Mexican jails are not fun to be around. People yelling at other people -- staccato Spanish, and the hands on the wall clock take an hour to move ten minutes.
Lewis has a priority telephone line to Qualitas in Tijuana and they in turn have a lot of sway with their main headquarters. I have seen this up front and personal. They get an adjuster to the police department in a rush, with a checkbook. There are always three Mexican agencies involved in a serious accident. A second adjuster and an abogado (attorney) who specializes in liability accidents deals with the family or the injured other party. If the family or injured rejects the settlement the whole process comes to a halt while the Ministerio Publico adjudicates the settlement. Your lawyer works with the ministerio publico (who does not want to wait for his payment) and together they can persuade the injured not to dilly-dally or risk losing a sizeable percentage of the settlement.
You want this to happen in hours, not days. Get the bono posted and get out of Dodge.
I do not know of Sanborn's reputation except they have been around a long time. And they must be good because there would be flak if they weren't.
I know of no Insurance company in the states that has no complaints against settlements.
I know my ins and outs down here but tangling with the ministerio publico is something I avoid like the plague. Their procedures and process are an unfathomable gordian knot.