Note that it doesn't take a huge amount of pre-planning for a ship location. He has posted the ST cycling route locations, so conversation can be something like, "Are you still going by way of Silver City/Las Cruces/Sierra Blanca? How far away are you now and how long are you expecting it might take?" and then "Ok, if you need, I how about I send you X to the post office at Y?" After that, send with his name to General Delivery with the town and zip code and give yourselves and extra day or two so he doesn't get stuck waiting for something to arrive.

Personally, I'd pick those towns that you sort of have to go through but I also don't pick the largest towns (e.g. El Paso). The reason is the post office is frequently pretty easy to find and you don't have much other choice. I don't know where he is now, but a quick look on the maps says some good candidates I might use would include: Sierra Blanca, Van Horn, Alpine, Sanderson, Del Rio. Hopefully he is tracking well to El Paso but if not, towns before that might include Silver City or Las Cruces.

I had a similar exercise on my first trip across the USA. I somehow went through both folding tires I carried and the second one went on backside of MacDonald Pass in Montana. I came into Helena on a Saturday evening after bike shop had been closed. I didn't really want to wait until Monday and instead called my parents to have them mail an extra spare folding tire I had at home to Miles City, Montana post office which was easy to pick up on my way.

I've had more difficulties with mail drop locations when you cross outside the US border since sometimes mail seems to get delayed for longer than you expect. For example, on my Canada trip, I had pre-arranged to pick up mail at Rivier-du-loup that seemed to be abnormally delayed. If I were to do that trip again, I'd likely pick a mail drop or two that involved briefly crossing to the US at places like St Ste Marie.