  Context. Galactic binaries account for the loudest combined continuous
gravitational wave signal in the Laser Interferometer Space Antenna (LISA)
band, which spans a frequency range of 0.1 mHz to 1 Hz.
  Aims. A superposition of low frequency Galactic and extragalactic signals and
instrument noise comprise the LISA data stream. Resolving as many Galactic
binary signals as possible and characterising the unresolved Galactic
foreground noise after their subtraction from the data are a necessary step
towards a global fit solution to the LISA data. Methods. We analyse a simulated
gravitational wave time series of tens of millions of ultra-compact Galactic
binaries hundreds of thousands of years from merger. This data set is called
the Radler Galaxy and is part of the LISA Data challenges. We use a Markov
Chain Monte Carlo search pipeline specifically designed to perform a global fit
to the Galactic binaries and detector noise. Our analysis is performed for
increasingly larger observation times of 1.5, 3, 6 and 12 months.
  Results. We show that after one year of observing, as many as ten thousand
ultra-compact binary signals are individually resolvable. Ultra-compact binary
catalogues corresponding to each observation time are presented. The Radler
Galaxy is a training data set, with binary parameters for every signal in the
data stream included. We compare our derived catalogues to the LISA Data
challenge Radler catalogue to quantify the detection efficiency of the search
pipeline. Included in the appendix is a more detailed analysis of two corner
cases that provide insight into future improvements to our search pipeline.
