Excellent explanation. We can get a little quantitative if we remember that the fundamental frequency of a vibrating string is sqrt(T/μ)/(2L), where T is the tension, μ is the linear density, and L is the length. So if we make the string twice as long, (T/μ) has to be increased by a factor of four; if we keep the tension the same we can use a string with 1/4 the linear density, which I guess would decrease the inharmonicity significantly.

The square root magnifies the effect of increasing the length, so you get a lot from making the piano a bit longer. The project is a wonderful idea.