Partial dataset with missing GCPs causing tilted model

[March Castle]

Hello,

I am having problems processing an incomplete dataset. This only features 4 GCPs in a straight line along the same axis, which I think is causing the model to be tilted - see screenshot.

The images were collected with a low resolution thermal camera (382x288 px) with an 8mm lens.

I have tried calibrating the camera and entering the lens and sensor values, but this did not solve the issue.

There is no GPS data in the image metadata, but they have aligned very well - the only issue is the projection.

 
The GCP locations were logged with a centimetre accurate GPS receiver, and I have verified that data is reliable.

Is there any way to correct this, or is the lack of GCPs on the other axis impossible to overcome?

Thanks for your help, March.