A burro pulling a cart is a very feasible idea, but not to carry you and your wife, just your gear and supplies, so keep following that line of thought.

The reason I joined this forum was to learn about lightweight gear and apply that to how I'd pack my burros. The lightweight cart idea is a great one, and there's a lot of tech out there to look at, like those horse racing carts. The same goes with all the gear you'll be using and a cart would be a primed place to innovate for a trip like this.

If it were me, I'd design a cart that would make it easy for me to help the burro tote the load.

A burro might get you further just because you have one too. They have a strong heritage there and I think the locals would be hard pressed not to admire you're embracing that.

A burro might in fact be key to your success.