We construct supersymmetric $AdS_3$ solutions of $D=11$ supergravity, dual to
$d=2$, $\mathcal{N}=(0,2)$ SCFTs, that are associated with M5-branes wrapping
two different four-dimensional orbifolds. In one case the orbifold is a spindle
fibred over another spindle, while in the other it is a spindle fibred over a
Riemann surface with genus $g>1$. We show that the central charges of the $d=2$
SCFTs calculated from the gravity solutions agree with field theory
computations using anomaly polynomials. The new $D=11$ solutions are obtained
after constructing a new consistent Kaluza-Klein truncation of maximal $D=7$
gauged supergravity reduced on a spindle down to $D=5$ minimal gauged
supergravity.