Change of ionic packing upon crystals are pressurized
Your termination of BCC is incorrect about the $\ce{NaCl}$ crystal structure upon pressurization. It is actually simple cubic (SC as $\ce{CsCl}$) where eight $\ce{Cl-}$ ions ate the corners of unit cell and one $\ce{Na+}$ in the center or vise versa. Although either $\ce{Na+}$ or $\ce{Cl-}$ in the center, it is not BCC because ion possessing the center of unit cell is different from the ions at the corners of unit cell:

Thus, lattice constant $a$ can be expressed as:
$$a_\mathrm{SC} = \frac{2(r_\ce{Na+} + r_\ce{Cl-})}{\sqrt{3}} \tag1$$
For FCC $\ce{NaCl}$ crystal structure:
$$a_\mathrm{FCC} = 2(r_\ce{Na+} + r_\ce{Cl-}) \tag2$$
Since $a_\mathrm{SC} \lt a_\mathrm{FCC}$, we can conclude that upon pressurization, $\ce{NaCl}$ crystal structure would be  contracted.