OMG you guys are making this too complicated.
Who wants simple, conservative-minded squide-factors during an actual dive?
It's much more fun to geek out about pointless, theoretical, mathematical pressure differences that are far too tiny to be measured accurately with the instrumentation produced for divers, especially given minuscule differences in tank manufacturing and which are heavily dependent upon variables like temperatures (which can frequently shift even mid-dive - think thermoclines and haloclines).
It's much, much more sensible to plan your rule of thirds based on what you actually have based on those careful mathematics based on actual gas behaviours rather than imprecise ideal gas laws. That way you can decide whether to split 107 cf into thirds instead of 116. That's a difference of a whole extra 3cf that could be used for an entire minute's penetration to be considered!