On a local variant of the 12th Delfino problem -- the $\mathrm{\Pi }$-side

Assume that $M_n$, the canonical inner model with $n$ Woodin cardinals, exists. We force a model with continuum ${\mathrm{\aleph }}_2$ in which every ${\mathbf{\Sigma }}_{n+2}^1$ set of reals is Lebesgue measurable and has the Baire property, the ${\mathrm{\Sigma }}_{n+2}^1$- and ${\mathrm{\Pi }}_{n+3}^1$-uniformization properties hold, and the reals admit a ${\mathrm{\Delta }}_{n+3}^1$-definable well-order. Thus regularity up to a fixed finite projective level, together with a definable well-order of the reals at the adjacent level, does not force the determinacy strength which would normally explain that regularity, even when this package is strengthened by adjacent $\mathrm{\Sigma }$- and $\mathrm{\Pi }$-uniformization. In particular, this gives a negative answer to a local form of Woodin’s twelfth Delfino problem asked by Friedman-Schindler.