It's possible to make sense of "1 second per second".
This just means a clock-hand shows a difference of 1 second, through '1 second' of qualitative/absolute temporal flow. They are two different things. Thus, it makes sense to say, of a second clock, that it evolves at 1/2 second per second, if its relatively moving or in a gravitational gradient. It is *also* possible to say the second clock evolves at 1/2 second per second and mean you're only comparing the moving clock's hand positions with a local stationary clock's hand positions. That's all relativity does.
But in the previous sense, of things evolving in qualitative/absolute temporal flow, the local stationary clock evolves at a rate of 1 second per qualitative second, or q-second. The moving clock, similarly, evolves at a rate of 1 second per *its* q-second. Its q-seconds are not ontologically comparable to the local stationary q-seconds. The qualitative/absolute time is ontologically ineffable, as argued for previously. The ontologically "effable" part of time is given by the relativistic correlations. There is no fact of the matter, or ontologically possible comparison, between different q-seconds.