I just skimmed through the papers that you mentioned. Wood and Moreau's scalar field looks like a state function and I am not sure if it would include a flow field and hence drag effects. The energy tensor includes both "pressure" and "density" terms. We are more familiar with the Sun's solar wind. The heliopause is where the solar wind meets the galactic wind; there could be particles attracted towards the sun that are masked by the solar wind closer in.

If a force is produced by the gradient of a scalar field, variations in the force might be produced by variations in the scalar field or some variation in the nature of space. So we have to consider an unknown field or changes in the nature of space. If the universe has a static pressure field, acceleration of the field towards the Sun would produce an imbalance in the field which might exert forces on a spacecraft.

I think that there is a bias in the procedure commonly used to find slopes and intercepts. One would have to run checks on the procedure one uses to do fits to determine if a systematic error is present or not and to what extent it can be trusted.