I cannot be helpful to you from direct personal experience in handling ESOP at retirement, but I found your question interesting so I did a little search. I think offering company stock can be such a good part of a company's business plan. But when a stock is not publicly traded, I assume the rules can be a little different at retirement.
As with any rollover or distribution, the retiree has to be careful in understanding the potential for tax consequences.
I came across the term NUA (Net Unrealized Appreciation) as a factor to consider in tax-treatment of an Employee Stock Ownership Plan. I did not read in detail though about NUA or how it applies.
Please bear with me for a few more sentences while I give you a little unsolicited advice. . .
Find a good tax accountant to help you. At retirement we often are circled by various types of financial "advisors" who want to be ever so helpful with where to put our money. They might even offer tax advice. But if I were you, I would pay a good CPA who should not be trying to sell you anything.
Take this step-by-step and your first step is to understand tax implications.
Before talking to an accountant, I would do some reading on the subject. Reading on the subject can help tremendously in knowing what questions to ask when making this important money-move.
If you are in Florida, there should be plenty of accountants who are quite familiar with ESOP. I am pretty sure that Publix offers ESOP. (When I got to Florida, I noticed that Publix employees overall are usually well-trained and pleasant. Somebody told me they can share in company stock. I then checked to see if Publix was publicly traded. Not.) (sigh) But I digress. . .so anyway. . .
There is a lot of information to be found with a google search. Here's a start:
ESOP Vesting, Distribution, and Diversification Rules
Also, please know that I have absolutely no qualifications to give financial advice. I am just telling you what I would do if I were you.