For a start, I would suggest you loosen the indicated pinch bolts, and push the bars forward a little, and rotate them outboard a little.
This is an adjustment, not altering the curve in the metal... the sketch is misleading.
By moving the bars forward in the indicated pinch bolts, you'll get more wheel-turn for the same movement of the handlebars.
Rotating the bars so they're further apart will give you more space before the bars stop on your seat.
And the best part - all that is completely reversible if you don't like it.
Modifying the push rods is going to be a lot more brutal and permanent. I'd start with a mock up using something cheap and disposable, perhaps plastic pipe or cardboard roll-centers temporarily.
I'm hedging a bit here but I THINK moving the pushrod at one or both ends will alter your steering like you want.
Downside is the width of the straight-ahead window will be much smaller, so you're going to have to actively steer a lot more when not turning.
Since its going to be very hard to change the steering arm on the wheel's hub, you might be better off checking with the supplier in case they offer any options to achieve your goal. A steering arm replacement with a hole that is closer to the kingpin would be much safer than you attempting to drill a new hole for the swivel. Note that the swivel will be a tapered hole too.
The safest solution would be to make an adapter plate that attaches to the main bar, and make two new shorter pushrods. That way you can revert to stock with no changes.
Also, consider making a scale model of the steering, using cardboard and pins to get an understanding of the relationships between your ideas and their effects.