You can get the Menaje for a one pass trip and there may be time limits and value limits on it. Formally, it make no difference what you tell them. Taxes are based on the valuation placed on the stuff by the Mexican Government. Even if you have reciepts they may not agree with the valuation. You will hear people brag all the time how they got receipts documenting half the actual value and the Mexicans are aware of this. As I understand it nationality makes no difference under the law. If it's used stuff it's iffy. If the total value exceeds a certain amount you are required by law to use one of the professional brokers who do the paperwork and all. A a big factor is who is manning the station on the day you cross. Some are easy, some are not. It a toss of the dice. Alternatively you can call Goff at Border Movers and have him take care of all of it, easy peasy. He will pick it up, move it down, take care of the paperwork and place it where you want and he knows what he's doing.
You might look locally. Stop by the consignment place there on Fremont they have a huge selection of stuff. Some of the condo owners who walked away from the condos stripped the furniture and took it there.
In my ignorence about 8 years ago I arrived with a pickup loaded and the largest U-Haul available. Mostly stuff I wanted to give away and some I wanted to keep. Nothing new, nothing fancy. Arrived after dark, got the green, started pulling away and was shouted to a stop by one of the inspectors. We opened the trailer and a bunch of junk fell out he kept saying I needed to have someone process it and I kept asking how , how much and who. He finally got next to the truck, leaned forward held his hand under his stomack and said, $200 under the wire. I paid at that point, crammed stuff back in and took off. As I was leaving Sonoita someone kept flashing their lights behind me so I puled over and was told the trailer door had slid up !! It was not fun and there was no discussion of lard involved at any point !