When you sell shares (no options involved):
If you plan to use any method besides FIFO, including LIFO, you must specifically direct your broker as to which shares to sell so that your taxes end up the way you want. According to Internal Revenue Service Publication 550, the burden is on you to prove that you informed your broker of which shares you wanted sold and that your broker followed your requests. If you can't prove that, you're treated as having sold your oldest shares first. See Zack's article.
I can't imagine that you could ignore this regulation if you sold covered calls and you were assigned, simply
tracking the cost basis myself, making Vanguard's FIFO irrelevant.
I've never come across a broker that allows you to specify lots when you write covered calls but I've only used about half a dozen brokers for options in 35+ years. And if that ability exists, the key question is, does Vanguard allow you to do so? Call them.
As I mentioned in my answer that you linked, when options are exercised, the OCC utilizes a "wheel" to determine who will be assigned. They notify your broker who has an internal process that designates who will be assigned (relevant prior to expiration). I believe that this will be FIFO and I question whether one can intercede in this OCC process. The only way to find out is to call your broker and ask if you have the ability to designate which of your shares will be assigned. I doubt that you can.
If the answer is no to all of the above then you have two final choices for closing the position:
If you can designate which shares are sold when you close a covered call via a Buy/Write order, then do it that way so that you can work the order for a more favorable exit price (call your broker).
If you cannot designate which shares are sold with a Buy/Write order, buy to close the short call and sell the shares that you want to designate (see the Zack's information above).