Supported sitting position

Koda
As you can see in the picture, my 3 1/2 month old baby (will be 4 months on January 29th) has all the strength she needs to be able to sit in a supported sitting position or "tripod" position, where she sits on her own by using her hands to keep her balance. 
But it is so incredibly difficult to get her to do it! She's very strong and really loves to stand unlike a lot of babies. Of course she doesn't stand on her own, but she has all the strength she needs to stand up without help, she just has zero balance and needs help so she won't fall over.
I know it can take up to 6 months or even later for a baby to be able to sit on their own, but I'm just trying to do a lot of exercises with her every day to make sure she does it on time (and as soon as possible) of course I keep all of her exercises lighthearted and fun, and make sure she is comfortable doing them.
I've tried putting a toy in front of her to get her to reach for it or bare weight on it with her hands, but it doesn't seem to help. She often cries when I attempt to put her in this position. I put her legs spread out wide so she has a large base to keep her balance, and I put her hands between her legs to hold herself up, but for whatever reason, as soon as I stop holding her up for her, she starts crying. I do it gently and make sure she has her balance, and I make sure she's in a safe place if she falls over. I occasionally allow her to tumble over to the side, which she doesn't mind at all, but I never let her fall face first or in an uncomfortable or unsafe way. So I think she has pretty positive associations with the position.
I've tried putting a pillow on her lap and she does sit up that way for a few seconds, but again she quickly gets fussy, and pushes her face into the pillow like she's rooting for milk (I make sure she's not hungry during these activities. She used to do the same thing during tummy time but she's gotten better now.) 
As I said before, she's very good at standing and likes doing it. So most of the time when I put her in a tripod sitting position, she pushes her legs down and pushes her back up against mine very hard, and starts trying to stand up and crying if I don't help her stand. If I didn't hand my hand or my chest right there when she does this, she would fly backwards very quickly, straight onto her back in a laying position. Which is why I put so much emphasis on making sure she's in a soft place when we do this... 
Again, I know she doesn't need to be sitting up yet. I just want to work with her and try to teach her to do it within time. I do it patiently and lovingly.
I just want to know if anyone has any suggestions on how to get her to sit in a supported sitting position without pushing backwards or getting upset.
PS: If she's not sleeping or doing tummy time, I hold her sitting upright in my lap in a very straight, comfortable position. She prefers to be in that position instead of laying down, so she is getting practice and I know her back is plenty strong enough to do this. We also do baby sit ups every single day, where I lay her down, and hold her by the hands/arms to pull her up into a sitting position. She loves doing that. We've done it since she could hold up her head.
Zephyr standing, using my chest for balance at 3 months old.