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We report ultra-deep, medium-resolution spectroscopic observations for four quiescent galaxies with log$_{10}(M_*/\mathrm{M_\odot })\gt 11$ at $3 \lt z \lt 5$. These data were obtained with JWST NIRSpec as part of the Early eXtragalactic Continuum and Emission Line Science (EXCELS) survey, which we introduce in this work. The first two galaxies are newly selected from PRIMER UDS imaging, both at $z=4.62$ and separated by 860 pkpc on the sky, within a larger structure for which we confirm several other members. Both formed at $z\simeq 8-10$. These systems could plausibly merge by the present day to produce a local massive elliptical galaxy. The other two ultra-massive quiescent galaxies are previously known at $z=3.99$ and 3.19, with the latter (ZF-UDS-7329) having been the subject of debate as potentially too old and too massive to be accommodated by the $\Lambda$-CDM halo-mass function. Both exhibit high stellar metallicities, and for ZF-UDS-7329 we are able to measure the $\alpha -$enhancement, obtaining [Mg/Fe] = $0.42^{+0.19}_{-0.17}$. We finally evaluate whether these four galaxies are consistent with the $\Lambda$-CDM halo-mass function using an extreme value statistics approach. We find that the $z=4.62$ objects and the $z=3.19$ object are unlikely within our area under the assumption of standard stellar fractions ($f_*\simeq 0.1-0.2$). However, these objects roughly align with the most massive galaxies expected under the assumption of 100 per cent conversion of baryons to stars ($f_*$=1). Our results suggest extreme galaxy formation physics during the first billion years, but no conflict with $\Lambda$-CDM cosmology.