According to USC 6601 — which is the current law — the President literally has the power to abolish USAID entirely, and only has to submit a report about it to do it. [1] Saying that closing the HQ and assigning a Republican as the head of USAID is "illegal" or "should not be possible without an act of Congress" doesn't make sense. Congress already passed an act allowing the President to terminate USAID. Congress does not mandate that USAID exists forever, and does not prevent the President from terminating it or streamlining it.

1: https://uscode.house.gov/view.xhtml?req=(title:22%20section:...

I have used it on Municipal Codes to explain things. I just don't have enough background on federal law and how amendments are stored.