I don't see any paradox here. (Although you conclude the same eventually)
"there is not the slightest interval between establishment of the mind, training, bodhi, and nirvana"
(Gyoji, in SBGZ, vol 2, BDK Edition, p 163)
Yes, there is no "paradox" in Shikantaza, although it does seem like a paradox. It is the seeming paradox of "original enlightenment", namely, if we are already "Buddha" why don't we know it and act like it? If there is "nothing to seek and do", does that mean that we don't have to seek it? (No, we have a lot of work to do!) Here is how I usually explain it.
We begin at the bottom of the mountain, lost in ignorance. We set our mind on escaping ignorance by climbing the mountain, training, climbing higher and higher to attain the wisdom and compassion of Buddha, and all the wondrous perfection of Buddha at the summit. Up up up we climb, step by step.
However, along the way, we realize that the entire mountain has been Buddha all along, top to bottom, although the fellow at the bottom and start of the climb did not recognize so until the fog of ignorance began to clear. Soon he realizes that each step along the path, right and left, up and down, walking smoothly and even falling in the mud or poison ivy sometimes, is itself total arrival at Buddha for all is Buddha all along. Buddha good at the beginningless beginning, good in the middleless middle, good right to the endless end. Each step (even the imperfect ones in which we stumble and fall, twisting our ankle) is perfectly Buddha too. There was never any place to "get", and each step is the finish line ...
... nonetheless, one keeps walking walking, climbing climbing, actually getting better at this Practice, closer to the summit, more "Buddha-like" with time ... clearing away the fog, getting better at avoiding the mud and staying clear, now much less likely to trip and fall down (although it can still happen to even the best climbers).
Better said, in this "climbing Buddha mountain", one comes to realize that it is in fact the mountain climbing you, you climbing you, climbing climbs climbing, mountain mountaining mountain, all Buddha Buddhaing Buddha. (So many of Dogen's word plays and bent grammar was just expression of this).
One has never actually gone any "place" cause always Buddha here and Buddha there ... yet the fellow at the bottom does not know it, the fellow at the top after years of climbing is so much better at it, ever closer to Buddha. Although all "Buddha Buddhaing Buddha", the difference between a climber on her first day, and a climber 30 years down the path is that hopefully the climber 30 years down the path is 30 years better at knowing and living this "Buddha Buddhaing Buddha", ever freer of greed anger and divisive thoughts, better understanding of the trail and how to avoid those mud puddles and the poison ivy of delusion. She knows too that we are "Buddha Buddhaing Buddha" if we just sit complacent at the campsite, but also "Buddha Buddhaing Buddha" when we move and get on with life ... so she gets up to live and continue to walk, but now embodying "Buddha Buddhaing Buddha".
When we sit Shikantaza there is only sitting as sitting sitting, us, us using us, sit sitting sit, "Buddha Buddhaing Buddha" ... no place to go, nothing more in need of attaining, all fully realized and resolved ... "Buddha Buddhaing Buddha". When we get up from the cushion, off the Zafu, crawl out of the tent and get on with life we now know that we are us living life, life lifeing life ... "Buddha Buddhaing Buddha".
Every step total arrival, yet walking on and on.