I can absolutely relate to your situation. When I first learned to play guitar I played seated all the time. When I built up enough confidence to try my first open mic, I was fortunate enough to be able to grab a stool from the bar.
But when I started playing in a band while also being the sound man, it was essential that I learn to play standing so I could move around stage and interact with the other musicians as well as get to the board to make adjustments when needed.
At first I experienced the exact same issues you are dealing with. But fret not - I was able to make some adjustments and with practice, eventually overcame the challenges - and you can too.
One thing that I would suggest is to position your guitar while standing in as comfortable a position as possible. Don't worry about looking cool, worry about your ability to play the darn guitar without missing notes.
You will most likely find that shortening the strap, holding the guitar higher, will make it easier to play while standing. If you keep your guitar higher on your torso, you will be able to apply a little pressure on the body with the forearm or elbow on your picking hand whenever you feel the need to tilt the neck towards you the way you can when seated. If the guitar is hanging too low, your elbow won't even be close to the guitar body.
Another thing to try is changing the strap attachment points which will alter the geometry of the guitar in relation to your body. One end of the strap will always attach to the strap button near the bout of the guitar body. It may be best to leave that one where it is. But the other end of the strap can attach near the heel of the neck where the neck joins the body, or on a horn on the guitar body, or even at the headstock using a leather tie string. Experiment with different attachment points.
Another thing you will want to do is get a comfortable strap. I like a wide soft leather or suede strap because it is more comfortable, and is less likely to slip around on my shoulder. Try a strap with a wide shoulder pad area and try shifting it away from your neck more towards the edge of your shoulder. I found that more comfortable for me.
Another thing that will help tremendously - is shifting the position of the guitar as it hangs from the strap so that the body is closer to your right hip (assuming you are right handed). This will more closely approximate the position of the guitar body when you are seated (and resting the guitar on your right leg). You will notice that when you rotate the guitar body towards your right hip, your wrist and arm on fretting side will be more in line and it will be easier to form the chords and feel more like playing seated.
Finally - practice practice practice! After you get a good comfortably strap that helps you position the guitar where you want it on your shoulder, and determine the best attachment position for the strap, and the most comfortable playing position for the guitar while standing, practice as much as you can playing that way. Even when you play seated, use the strap - so the guitar is suspended from the strap versus resting on your leg.
What I found is that over time, I got to a point where I could play just as comfortably standing with a strap as I could sitting on my couch with the guitar on my knee. I am confident that you will too.