Do the gyroids in Club LOL have any affect on the songs played in Club LOL

My village's "Re-Tail" closes at 11pm, so I went to visit tonight near closing time. Aside from another villager being present at closing time, nothing out of the ordinary happened. I continued waiting for a few minutes...

...and was not asked to leave. So if you have any business to conduct at Re-Tail, so long as you get in the door before closing time, you'll have plenty of time to take care of things. If the developers created any special events for when Re-Tail closes at night, it is not obvious or within the same time interval as previous AC games.

As a point of note, the lights were out and the shop was closed upon my exit.

The Music Box

The Music Box is actually a family of furniture items, only obtainable by the method you mentioned. Like all other furniture from Cyrus, it is not possible to take one of his products apart into the original materials/furnitures used to make it.

When Cyrus creates the Music Box, the result is a colourful version of the Giant Clam Shell that, whenever opened, will play a little music-box-like version of your song, before closing shut once more.

You can think of the Music Box as a larger, physical, standalone counterpart of the song used to create it, as the Music Box will retain its name when created.

Additional Copies of Music

As for obtaining another copy of the song, if you have access to the Timmy & Tommy Shopping Catalog from upgrading the Nooklings' shop at least once, you'll notice that there is a category in the catalog for music.

Although you cannot order Music Boxes this way, all of the K.K. records you have ever received or will receive in the future will be recorded in the catalog. Each of these records can simply be ordered from the catalog for 3,200 bells.

Therefore, by purchasing your additional copies from the catalog, you are free to request new pieces of music from K.K.Slider each week.