Hello Rubix,
The problem is almost as difficult as the cube you invented!
The regulations require the nose load of a trailer to be greater than 25Kg (EU specified minimum) but less than the lowest upper limit specified by the the car, tow ball and caravan manufactures. It is generally accepted that towing stability is maximised when a nose load close to the permissible limit is achieved.
The other important EU specification says that the when attached to the tow vehicle and both are loaded and ready to tow, the centre of the tow ball must fall between 350mm and 420mm above the the surface of level (Horizontal) ground. As these regulations are law, and they specify limits, there is no margin for error beyond those limits.
The consequence of being outside the limits is that by definition the outfit is legally not road worthy.
I can understand your frustration on this matter. The fact is, it is far quicker and easier to measure the actual nose load than to try and calculate it. The use of bathroom scales with a suitable piece of wood (and spreader to avoid damage to the scales) is a perfectly acceptable method provided you can allow for the uncertainty of measurement of the scales.
But lets try to be practical here and find a solution for you.
For reasons that have be explained elsewhere in the forum, the nose load of the trailer will vary depending on how high the hitch is compared to the road wheels. The nose load increases if the hitch is lowered, and decreases if the hitch is raised. The degree of change is difficult to calculate, but it is significant if it means that under regulation measuring conditions the nose exceeds the permitted maximum.
The regulation condition require the caravan to be on a level (Horizontal) surface. The hitch height is measured vertically from the horizontal to the centre of the ball. So relying on the fact that nose load greatest when it is at it lowest height, then if the load gauge is set to give the minimum hitch height of 350mm then at all other regulation hitch heights the nose load will be slightly lower.
As the hitch height has to measured from the horizontal line from the road contact of the wheels, any slope of the ground compromises the use of a fixed 350 mm length gauge. What you need to do is to establish how much height is lost or gained as a result of the slope over the distance between the hitch and the wheels. If you then change the length of the gauge by this variance, when the hitch is lowered onto the gauge the required 350mm elevation above the horizontal will be restored, and the nose load measurement will regain its accuracy.
The gauge will only remain accurate provide the measurement is taken on exactly the same slope, and in the same direction, and with a caravan that has the same hitch to wheel dimension.
I hope this helps.