Would including the true/known y-intercept in my dataset be "overfitting"?

[FactChecker]

That can be done, but it has to be a very explicit and convincing argument. Personally, when I see a statistical model done without an intercept I am instantly highly suspicious. The burden of proof is on the scientist much more stringently, and frankly in some infamous papers where I have seen this done it was done poorly and rendered the conclusion completely unbelievable.

So overall, my opinion is opposite yours. I would rather use a standard and reasonable statistical process and look at the fitted intercept as a check on the quality of the data and the model.

I think that I have to concede that your approach is the wiser approach. Forcing the Y-intercept to a particular value would only be appropriate if there is indisputible consensus based on science.

 

[Rap]

The problem is stated mathematically as:
ε²=Σ(m x_i+b-y_i)²
b=7
Minimizing the mean square error (ε²)
dε²/dm = 0 = Σ(m x_i+b-y_i) x_i
Solve above for m and that’s your fitting equation, y=mx+7. m will be expressed entirely in terms of known quantities with a guaranteed intercept of 7.