FFT with day-periodic data
Saying "7 samples per week" is perfectly reasonable.  The FFT doesn't care how the rate is defined, it only requires it to be constant.

When I fiddle with really low rates, I use the same concept.  Say, samples per minute or samples per year.  

Mathematically, it doesn't matter.  You know yourself that the number 1/86400 samples per second is mathematically the same as 7 samples per week - you calculated them both, after all.

The only effect it will have is in how you translate the FFT bins into a frequency - and you have to do that anyway, regardless of how you represent the sampling rate.

For myself, I find it easier to think of the numbers and samples when represented as some whole number of samples per time unit.