However, my error bar plots are X Error bars and the relevant error bar styling settings in the Plot Details dialog are not available for X Error bars.
Am I totally out of luck? Can this be done via LabTalk or X-Functions?
I am afraid that x error bars can not be drawn as lines. I can add a feature request to see whether we can improve to support it in the future.
As a workaround, perhaps you can plot the error as Y error bar as line and then exchange x-y axis to show the effect. You can select Graph: Exchange X-Y Axes to exchange axes