Schwarzschild and FLRW-coordinates

The construction principle of the radial Schwarzschild-coordinate \(r\) is to maintain a constant scaling of surface areas proportional to \(r^2\), whereas this is not done in comoving FLRW-coordinates, where the scaling of physical distance with the scale-factor \(a(t)\) is central. Could you construct FLRW-coordinates for curved Universes where \(\Omega_K\neq 0\) with the same idea of absorbing curvature into a newly defined radial coordinate? How would that coordinate be related with the scale factor to physical distance?