I was told once of a ship that had taken a missile hit, was on fire, and flooding. A sailor pulled himself from the burning compartment, only to be chastised for being 'out of uniform.'
Such is happening here. All this focus on the box at the end of the cord - when that's the least of the issues. Nor will that code citation help where you need to address your concerns - to the top end of the install!
Such drops used to be easy - hang a 4S from building iron, hang a Kellems grip from the hard ceiling directly above the drop, and punch a hole in the ceiling tile to let the cord pass. We can't do that now, because we are not allowed to have the flexible cord above the ceiling.
There are various brackets for mounting stuff to the grid, but IMO they're not up to the loads that this application would provide. Ceiling grids are not made to carry 'live' loads.
The best I can figure is that you make a 'tile' out of (at least 1/2") plywood, and support that as you would a light troffer. Run flex or MC to an "old work" box you mount to the board. Modify a 4S blank cover so you can attach it to the box, and attach your cord grip to the modified cover.
If you also cover the face of the plywood with FRP, it'll look a lot nicer. You can paint the 4S cover with 'appliance enamel' or 'spray lacquer' for a particularly nice finish.
Now ... for that pesky 'free hanging' end .... We have none other than our Joe T to thank for the code section, for he spent the better part of a decade showing pictures of used, abused, and damaged 4S boxes on the ends of extension cords. His crusade also led directly to two other code requirements- that devices be attached with two screws on 'industrial' covers and that the covers have flat corners for 'better' grounding at the attachment points.
The code section does not require the use of a box at all - a free hanging connector would be compliant. A purpose-made receptacle assembly with a clamp would comply; Woods makes just such a thing. You could even have the cable go directly into a fitting on a machine.