Can one have prior years’ United States income tax refund carried over to later years?

Forms 1040 and 1040-NR allow overwithheld tax to be refunded via direct deposit onto a U.S. bank account or mailed as a check. However, there is a time limit for direct deposit. For example, see the instructions for 2019 tax returns for Form 1040 and for Form 1040-NR:

If any of the following apply, your direct deposit request will be rejected and a check will be sent instead.

• […]
• You file your 2019 return after November 30, 2020.

I want to regain overwithheld tax for the last three years: 2017–2019. (Tax paid earlier is no longer refundable.) The time limit makes it impossible to receive this money via direct deposit.

In my case, I have no ability to cash in a check as I do not reside in the U.S. (nor ever have) and checks are not accepted in my country, so I want to receive the money in some other way. (I am a U.S. “nonresident alien”, and my taxable income comes from dividends of publicly traded US company stock. Form 1040-NR is specifically designed for nonresident aliens, but it still only allows refunds to be mailed as checks past November 30.)

Besides direct deposit and check, the form allows another way of handling the refund: I can choose to have it “applied to [my next year’s] estimated tax”. I can then treat it as overpaid tax in the next year’s form. By chaining this far enough, I could have all my refundable tax carry over to 2020 or 2021, where I could get it all refunded to my bank account by filing a tax return within the direct deposit window.

• Is this allowed beyond November 30 and, more generally, for the whole three years that the tax return can be filed as a prior year return?

• What is the cheapest and quickest correct way to use this for multiple prior years? Do I have to submit 1040-NR for each year in order, wait for it to be processed, and only then submit the next year’s return? Or can I submit all three years’ forms (or four years’ together with the upcoming 2020 form) simultaneously? In that case:

  • Can/should I compute and specify the accumulated amount from earlier years in each year’s form’s “Payments: 201X estimated tax payments and amount applied from 201Y return” field, or should I leave this field empty?

  • Accordingly, can I submit the forms for 2017–2020 simultaneously (in early 2021) and immediately have the total amount refunded onto my bank account, or will the prior years’ accumulated refund have to wait until the 2021 tax return in 2022?

  • Can/should I send the forms all in a single envelope?

    Note: I do not have an ITIN yet, so I will need to send at least one of the tax returns together with Form W-7 to apply for my ITIN.

There is a similar question for Canada, but I am interested in U.S. tax returns.