Everyone I know regarding this issue says the safe answer is for the employer to issue a 1099-B if the employer is buying shares from people who are exercising their put option right under an ESOP.
This might be more answer then you want but here goes.
This means that if the ESOP distributed shares to X worth $10,000, and then Company Y bought thsoe shares for $10,000 the safest answer is the following (I am skipping the NUA issue to keep it simple):
The ESOP issues a 1099-R showing a gross distribution for $10,000. The company issues a 1099-B showing gross proceeds from a stock sale of $10,000.
The best trust companies that work regularly with ESOPs will tell you this is the way they want it done if they are the trustee of the ESOP. Then again they don't want to be sued and they are spending their client's money to issue all these 1099s to protect themselves.
I have never actually had anyone raise your specific issue. How many times, or times per year does one need to do this activity. So I have no specific knowledge as to how some of the people I have talked to over the years would answer your question.
But one of my opinions about many of these questions on this board is they are being over thought, or people are looking to rationalize a way out.
I would apply te KISS principle to most of these questions, Keep It Simple Stupid. To me the simple answer is if you are redeming shares every time someone is paid from the ESOP you are doing it on a regular basis. Issue the 1099-B from the company.
I have never been part of a stock buy for a note so I can not help you on that one.
Hope that helps.