Getting my household items into Mexico

You might want to look into something called a menaje de casa. If you get a new temporary or permanent resident visa, you're allowed to bring in your household goods that ordinarily you wouldn't be able to without tax. But you have to do it within a certain number of months, and there's a certain process you have to follow. I haven't done it myself. I think it involves documenting every single item you're bringing in, and possibly getting the list certified at a consulate.

Maybe you could get the stuff to the border and import yourself, with the menaje de casa, then ship domestically from the border town.