My advice would be to go to a rolfer and tell them about these issues.

I actually have a sit stand desk. And do use it some. But I have some issues with my hips and SI joints. Standing without walking gets painful pretty fast.

It can sure get painful quickly. A few things worth considering:

• Do you use one of those dedicated mat to stand on? I don't know the English name for those, but they do sell padded mats made to stand up on them. They help increase the duration of my standing position. Even more so if you also regularly switch your weight form one leg to the other, or just move on that mat. Get a good mat as it will help more.
• Don't force yourself to make long standing sessions, make them shorter but more frequent? Standing should not hurt.
  For me (50+ dude that was in really poor shape and health when I started), what matters is to regularly get my ass out of that chair for 10 or 15 minutes, sometimes more but as long as I have my 10 minutes I'm happy. Be it to stand at the desk or to do stuff around the office/home. It's the regularity, making it into a habit, that I find the most helpful. At the beginning I used a timer to remind myself to stand up and, yep, it was a pain to get constantly interrupted by that stupid alarm but since it seemed to help my back (edit: and knee and feet) a little I kept on using it up until the day I realized I needed it no more. I don't think about it, I just regularly move my ass out of that chair — ad I use one of those mats I mentioned.

I don't know about your specific situation so this may not apply at all, but getting back into walking also helped me immensely (as does help wearing good shoes: the day I switched to better walking shoes my endurance skyrocketed). That and healthier eating habits were key in me getting back into some kind of shape and health despite starting real low: I barely could walk at all.

Not exaggerating, I celebrated like if I was Armstrong stepping on the Moon, the first time I managed to walk down and back our street without being exhausted and without my joints, back and feet hurting so much for the next few days that I had to lay down (it was that bad). Nowadays, I walk up to 10 km daily, never less than 6. Sure, I'm no athlete and my health issues won't go away ever but what matters is that most of my chronicle pains have vanished almost entirely, even the most enduring ones that plagued me for... decades. And I can move around and use my body almost normally. I also lost a hefty chunk of fat, which is a neat bonus ;)

Sorry for that too long reply to your comment. It's just something I consider so worth talking about ;)

Invest in a treadmill. /s