One of the key aspects when simulating the plasma edge is the treatment of the neutral particles. Neutral particles can be described by a kinetic equation, which is difficult to solve due to the high dimensionality of the phase space and the high collisionality between the neutral particles and the plasma background, especially in the (partially) detached regimes anticipated for future reactors. We consider a recently proposed hybrid fluid‐kinetic method that is based on a micro–macro decomposition of the kinetic equation and mitigates the problems related to both the high dimensionality and the high collisionality. However, this method is prone to cancellation errors due to the introduction of particles with both positive and negative weights. In each iteration of the method, the particles undergo a weight projection step, which we identify as the main source of cancellation errors. We use techniques from numerical linear algebra for solving ill‐conditioned linear systems to improve the numerical stability of the weight projection step and reduce the cancellation errors. The reduction of cancellation errors allows for further speedup in the hybrid fluid‐kinetic method.