It seems like the default range/distance for GetHitResultAtScreenPosition is 10,000 units. Is there any way to increase it, or will a line trace have to be used?
Apparently this is a supporting method for GetHitResultUnderCursor and uses a distance specified by HitResultTraceDistance in the APlayerController class.
So this line trace range can be modified by setting HitResultTraceDistance (10,000 by default) in the PlayerController from which you are calling the line trace.
If you have a blueprint class wrapped over the PlayerController then you will need to set the value Mouse Interface → Trace Distance under the blueprint class defaults.