The primary (if not only) alternative to US employment law you will have access to is simply a written employment contract, which both the employer and employee sign and thus agree to be bound by.
These employment contracts are relatively common at higher-level positions, and are commonly used to define severance packages, minimum notice periods, the time length of employment, guaranteed pay and/or bonuses over a specified time period, etc.
The best way to approach having such a contract is to decide what you want in it, such as a mutually binding notice period (i.e., that unless some law has been broken both sides agree to give 1/2/3 months of notice or equivalent pay, etc.), minimum time length (agreement to employ no less than X months/years, with some penalty to be paid unless both sides agree, etc.), or whatever you find important to you.
You would basically say that, given the change in employment law and your dependence on a visa, you would like to request an employment contract with the following provisions, and then you list what you would like.
The company's willingness to negotiate is purely up to them, and in these kinds of contracts a lawyer will generally need to draft the official document, and you can put pretty much anything you want in it. "If I quit with less than 1 month of notice I promise to mow the CEO's lawn for 1 month," etc, whatever either of you want to put in there. A US lawyer for the company would almost inevitably be involved in the actual drafting and review of it before anyone at the company would sign it, so I can't say that it would be worth it for you to try to draft any legal document on your own.
Some companies, for some positions, do this all the time. On the other hand, the very design of work visas like the H1-B, H2-B, OPT, and L1 are intended to provide employees which are highly dependent on their employers's desire to hire them. The short notice and ability of employers to cancel their sponsorship for little to no reason is intended by the government to act as an axe hanging over the head of anyone holding them and so serve as motivation (and a boost to US corporate profits, of course).
However, not all companies have quite the same mentality as our nation's politicians and lobbyists. Decide what you would like, ask for a contract, and see how they respond. They can say no, at-will only, and you'll have to decide if you are still interested in the transfer. They can also decline any given contract item, or stuff the contract full of so many terrible clauses (including terms that wouldn't be legally enforceable anyway) that you'd be better off not having one at all, so make sure to read any such agreement in full! Consider having a lawyer looking at it as well, if you aren't comfortable with any of the provisions or legalese.