The self-channeling deflection of azimuthally perturbed Gaussian laser beams in xenon and helium gas jets is investigated using a modified model that incorporates the laser intensity-dependent ionization properties of the gas medium and the resulting different electron plasma density from the initial gas density profile. Simulations show that the deflection behavior in realistic gas targets differs significantly from that in preformed plasmas with the same density profile. The channel propagation behavior varies markedly with the addition of odd mode (), even mode (, , etc) and other higher order odd (, , etc) modes. Gas species and laser parameters strongly affect self-channeling deflection. Under the conditions studied, compared to xenon gas, self-channeling in helium targets shows significantly reduced deflection and longer propagation distances. At laser intensities corresponding to the ionization plateau of the target gas, a larger initial vacuum focal spot enables long-distance self-channeling by suppressing channel deflection. These results highlight the importance of high beam quality, particularly the suppression of odd transverse mode (), and the optimization of laser parameters, including a larger vacuum focal spot, and appropriate gas for achieving stable laser self-channeling.