Here are a couple of ideas…
One would be to change the Box Style in the Style settings to ‘Offset access’. You can also set exactly how much of an offset. The ‘Specified’ option is set up to scale with the point size to avoid the axis overlaying point. However, this does not draw the rest of the box.
Instead you could specify the tick mark locations.
In your data it looks like the x-locations are exactly where you would want the tick marks. Change the X tick marks setting to ‘Labels’ and then choose that column as your major tick marks and the same column would be used for the labels.
Also, continue to add a number less than zero for Include in x. Because zero is a special number, the default is to snap to 0. Including something slightly less than zero is enough to stop the default behavior of snapping to zero.
The graph above will only have major tick marks. If you also want the minor tick marks shown, Add an Extra Axis command and change the Drawing style is to ‘No labels’.
Does that help?