@Pipecarver I know you are looking for the bottom line, I'll keep this as interesting as I can.
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Far Red is off the chart to the right. The only hope of photosynthesis is Chlorophyll a and even that is insignificant. So this is not about standard plant to light responses in terms of making sugar.
It is a signal. Specifically phytochrome Pfr
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For any one phytochrome, there exists a photoequilibrium of two interconvertible forms, red and FR absorbing forms (also known as Pr and Pfr, respectively). Pfr is the active form of phytochrome and it elicits physiological responses
Source
So you are flipping a switch in the plant from one state to another.
This is the "put them to sleep faster" switch you are wondering about.
With me so far?
Probably not so here is the bottom line: For your use you need a fair amount of far red to cover the whole canopy to be effective in a 30 minute burst. In my testing a puck is insufficient for this purpose.
I'm tagging in
@Bandit420 in case he can say it plainer that me, or has a different experience.