Separating the individual elements in a music mixture is an important tool in computational musicology, allowing for an improved analysis of music repertoires. In the context of Carnatic music, this task remains a challenge given the suboptimal generalization of existing music source separation systems to this style. Although multi-stem Carnatic recordings exist, these are mostly collected from the mixing console in live performances. Therefore, there is an unintended presence of other sources in the background of the audio signal of an individual instrument. Another challenge for Carnatic music is the strong melodic correlation between the singing voice and the violin, two sources widely found in live performances of this repertoire. Existing strategies to address such problems struggle with source quality and only consider vocals. In this work, we propose to incorporate two components in the regular training scheme of a source separation network, namely a learned loss and a mixer model, to account for the source bleeding. We achieve improved separation while extending the separation targets to the violin, an important source in the repertoire, and therefore cover the separation of the most common melodic components in Carnatic Music. Code and models are available in compiam.