I've been rather busy with work the last two weeks, but here's what I've come up with in my spare time on the car search.
From my original list of compact hatchbacks, it looks like the following have the most accessibility options either standard or as part of a manufacturer's after-market mobility program:
Ford Focus 5-door
I could not find much information about accessibility for the Hyundai Elantra GT or the Mazda 3, which were both on my original list, so I've moved those two into the "research further" category. It looks like the Honda Fit, which was the 5th candidate on my original list, has very few accessibility options, so I've removed it from my list.
I also looked into the crossover segment, but have determined that will require some careful measurements. For example, another family member's Kia Sedona is "too high" for this relative to get out of. She feels uncomfortable since her feet cannot touch the ground when she gets out. The Sedona has a 6.6" ground clearance and 6' overall height, so it is not a massive vehicle. If she has difficulty with that, I feel she'll likely have difficulty with most of the crossover market.
My next round of research will be into regular sedans that might be a bit higher, like a Honda Accord, Toyota Corrola or Camry, Ford Fusion or Taurus, Hyundai Sonata, and so on.