  Recently, high-resolution spectroscopy of slow beams of metastable helium
molecules (He$_2^*$) generated by multistage Zeeman deceleration was used in
combination with Rydberg-series extrapolation techniques to obtain the lowest
rotational interval in the molecular helium ion at a precision of 18 MHz
[Jansen et al. Phys. Rev. Lett. 115 (13) (2015) 133202], limited by the
temporal width of the Fourier-transform-limited laser pulses used to record the
spectra. We present here an extension of these measurements in which we have
(1) measured higher rotational intervals of He${_2}^+$, (2) replaced the pulsed
UV laser by a cw UV laser and improved the resolution of the spectra by a
factor of more than five, and (3) studied $M_J$ redistribution processes in
regions of low magnetic fields of the Zeeman decelerator and shown how these
processes can be exploited to assign transitions originating from specific
spin-rotational levels ($N^{\prime\prime},J^{\prime\prime}$) of He$_2^*$.
