Even outside the VA, any PALS on Medicare or a commercial plan can obtain an order for a hospital bed with reverse Trendelenburg (cardiac chair) functionality and pay the difference from the reimbursed rate. And as you say, some of the Hillrom beds have this functionality. They are typically labeled as advance or ICU beds. But other less pricey brands such as Joerns have similar ones, just that they are not as heavy duty as a hospital bed that is moved between rooms and floors a lot.
For you, this kind of bed enables a seated position where your legs are bent and hips relaxed so you will not slip down. Many PALS also use extra pillows behind the back for additional support when they will be upright for a while.
I would think if your doc can write a letter of medical necessity for that type of bed, you might not have to pay extra in the VA's system --- will let the vets weigh in on that. But even if you did, it would be worth it.
I have attached an example of the ["four function"] remote that this kind of bed would entail. After raising the legs enough not to slip down you tilt the bed up and then adjust from there.