At least the EBT also do not teach there is nothing stable. There is that stable element of asankhata. But seeking stability in khandha’s or in constructed states, is not wise (dhamma eye sees this, i believe). The stable is arrived at when there is no grasping at arising khandha’s at all. The stable must have another base then khandha’s, fleeting formations.
Some buddhist take happiness or peace as the Path, like the Buddha also did.
He identified all that brings disease, unhappiness, lack of peace, burden. He removed it.
I believe this also means that Buddha, but also we, already know the peace of Nibbana, the unburdened, cooled, pure state, otherwise we are unable to identify those things that defile and cause burden and suffering.
We are not ignorant about Nibbana, we are ignorant in the sense we ignore it and do choose the wrong ways to happiness and peace.
When we practice according the teachings, i believe we cannot arrive anywhere else then in in this open (not grasped) dimension of coolness and peace. I think we can also say that is our true self, as our home.
This does not mean we have to regard peace and coolness as ourself. But we must just focus on removing defilements and the natural result will be Nibbana, our home.
A Buddha also shows a lot of control, much more then we do. He can even duplicate himself, and all kinds of amazing things. It is even said that if he wishes he can live much longer then a human can. Even for an eon.
To see rupa, sanna, vedana, sankhara, vinnana as not-self is, i believe, only a way to cure grasping and guide us home to Nibbana, the cooled state of peace without grasping, which is the end of the taking up of the burden in this very life.