Namaskaram, I also have had similar doubts regarding this sir. I have read the following:
1. That Aachamanam is meant to be done not sitting but kundhittu, with arms between muzhanthalgal.
2. And pranayama, sankalpa etc have to be done facing north or east generally (and while sitting in sayam sandhya I assume).
3. Argyam has to be given sitting, facing west, but we do pranayama and sankalpa for the prayaschitta argya which have to be done facing north no?
4. Then we would have to turn to the west again for the actual arghya.
(and then there is the actual aatmapradakshina-parishechana)
5. Then turn towards north and get on our feet again for the aachamana
6. And then sit towards north for the navagraha keshavadi tarpanam.
7. There is another aachamana recommended after this, before uttara bhaga, where I have even more confusion. Apologize for the wall of text, but I feel there is really no other place to discuss all this, as vadhiyars also seem not very interested in 'wasting' their time with boys learning sandhyavandana.