[politicket]

The Fed can purchase Securities directly through Open Market Operations (FOMC IIRC)

That's true. But they can only purchase them from approved dealers, not the Federal government.

This means that the bank in my example would have to buy the Treasury securities first, so that the Fed could buy them through a Permanent Open Market Operation (POMO) - and then create Federal Reserve notes as liabilities against the securities.

How would the bank afford the $2,000 on new securities in my example, without using some of its loan papers as assets for the purchase?

[Ghost of Philip Marlowe]

Are you forgetting that the entire system is based upon fractional-reserve banking?

Any “borrower” only needs to have 10% of actual reserves. They can borrow up to 90% against whatever they have.

When they do borrow, whatever they lend out, they consider that an “asset” which serves as security for future loans.

Yes, “debts” are assets in this scheme.

[count-your-change]

It could buy overnight funds from banks that had excess cash on hand.

The bank that needs extra cash pays a fee to buy extra funds before it balances its books at end of days business and returns the funds the next morning.
Next day the same thing happens if the bank still needs the extra fund and the next and the next.
But paying fees eats into profits.
Flying these “funds” around the country was, years ago, FedEx’s main business. FedEx purchased a fleet of small jets and was able to keep the very schedules this paper shuffle required.