What can be added to non dairy milks to extend shelf life

I make a pretty large quantity of homemade mayo and have never had a problem keeping it longer than that -- Good Eats uses a week for their recipe and for me it lives a month, easy, with no detectable reduction in quality. There really is enough acid and salt to deter most bugs if you like it strongly flavored (and let's be honest, mayo should be strongly flavored because it's a sauce made of fat and you might want to minimize the quantity applied). I'd also take the advice of stilltasty.com that while color, flavor, or texture may change it's generally still safe to eat refrigerated mayo even after it's notional "use-by" date.

In short, I strongly advise more salt and acid if you're worried (and also because it's tasty), but I also strongly advise a lack of worry.

I'd never heard of ESL until your question, so I had to look that up. A local company did a lot of work developing UHT milk; I remember samples when they were first starting up production, and they were trying to find flavors additives which would mask the flavor change from the UHT processing. Since then a lot of companies have adopted the processing methods for other products, or just adopted the packaging. So, before I relied on any random box-packed product to be shelf stable, I'd check into how it was produced.

Proper UHT milk doesn't go bad until it's opened. It's sterile, and in a pretty sturdy container. Once opened, bacteria will get back into the container, and the milk will go bad as normal. When the local company started production of UHT milk, they were putting 2 year code dates on packages, and that was just the longest date the government would allow; I've had boxes 3-4 years old, which were fine.