Respectfully snipped by me for brevity.
I think that Cheryl parked where she did either:
1. For the sole purpose of texting her carpool buddy. She realized that she didn't have her badge with her soon after leaving home, pulled over so she could text her carpool buddy, intending to drive back home, retrieve her badge, drive back and park at the P&R itself or somewhere nearby. However, something went wrong after she sent her last text.
or
2. So that she would not be seen by her carpool buddy, yet at the same time to leave evidence of her actually having been in the same area where her car would actually be found (by way of pinging, since her phone was still powered on at this point).
I do not believe it has ever been reported exactly where Cheryl was supposed to meet her carpool buddy[/B]. But if it was going to be inside the P&R, it makes sense that she parked where she did: There would be little chance of her carpool buddy witnessing Cheryl getting out of her vehicle. She would have avoided parking inside the P&R in order evade the security cameras, too, I think.
Like seemingly every other aspect of this case, there is more than one plausible theory or explanation here, IMO.