We spoke with an AUS tax lawyer who advised us:
Foreign pension fund contributions – if you did not need the cash, you could agree in advance with
[employer] that they pay an amount (whatever you agree on, say $50,000 pa) into your foreign pension
fund (perhaps a US 401(k) plan). This amount will not be earned as salary and so will not be taxable to
you. I would strongly recommend you discuss this strategy with them to save you substantial Australian
tax. It will save your marginal tax rate (expected 37% after your other salary sacrificing) times the
amount you sacrifice into an offshore pension fund. So if you were to salary-sacrifice say $50,000 pa into
a US pension fund, you would save around $50,000 pa x 37% = $18,500 pa in Australian tax. Over four years,
that is an expected personal tax saving to you of $74,000.
What kind of funds... could we put this money into? It is my understanding that we could no longer contribute to our 401(k)from our former employer. Are there negative tax implications in the US to doing this?

This strategy needs to be discussed IN DETAIL and FACE-TO-FACE with a competent tax professional in the United States, as there are all kinds of implications in this strategy.

For one thing, there is a cap as to how much you as an employee and your employer can contribute to the 401(K). I believe it is $16,500.

There is also considerations as to whether the pension plan is qualified or not, plus non-discrimination issues which dictate that highly-paid employees cannot receive preferential treatment over lower paid employees.

The implications are mind-boggling and WELL BEYOND the scope of this forum In my opinion.

Thank you for your response. We are seeking further clarification from a tax professional.