I always play with a strap seated, both acoustic (and electrics, many years ago.). Always hated the way the guitars didn’t feel properly supported, the neck moves around, and feels like it wants to slide off my lap.
That said, I very recently discovered I can “pin” my acoustic to my right leg with the weight of my right arm, if lower the headstock enough.
Picture and explanation here:
I still play with a strap…for me, having the headstock so low disrupts my fretting hand, and I have to slouch to securely pin the guitar. But it might be something to experiment with if you don’t like a tighter strap.