  We present results from MeerKAT single-dish HI intensity maps, the final
observations to be performed in L-band in the MeerKAT Large Area Synoptic
Survey (MeerKLASS) campaign. The observations represent the deepest single-dish
HI intensity maps to date, produced from 41 repeated scans over $236\,{\rm
deg}^2$, providing 62 hours of observational data for each of the 64 dishes
before flagging. By introducing an iterative self-calibration process, the
estimated thermal noise of the reconstructed maps is limited to
${\sim}\,1.21\,$mK ($1.2\,\times$ the theoretical noise level). This thermal
noise will be sub-dominant relative to the HI fluctuations on large scales
($k\,{\lesssim}\,0.15\,h\,\text{Mpc}^{-1}$), which demands upgrades to power
spectrum analysis techniques, particularly for covariance estimation. In this
work, we present the improved MeerKLASS analysis pipeline, validating it on
both a suite of mock simulations and a small sample of overlapping
spectroscopic galaxies from the Galaxy And Mass Assembly (GAMA) survey. Despite
only overlapping with ${\sim}\,25\%$ of the MeerKLASS deep field, and a
conservative approach to covariance estimation, we still obtain a
${>}\,4\,\sigma$ detection of the cross-power spectrum between the intensity
maps and the 2269 galaxies at the narrow redshift range
$0.39\,{<}\,z\,{<}\,0.46$. We briefly discuss the HI auto-power spectrum from
this data, the detection of which will be the focus of follow-up work. For the
first time with MeerKAT single-dish intensity maps, we also present evidence of
HI emission from stacking the maps onto the positions of the GAMA galaxies.
