The harmonic multiplying operation in a gyrotron traveling-wave amplifier (gyro-TWA) permits magnetic field reduction and frequency multiplication. This study presents a comparative analysis of fourth-harmonic multiplying gyro-TWAs with three schemes of operation. An improved mode-selective circuit using circular waveguides with various radii provides the rejection points within the range of operating frequencies to suppress the competing modes of gyro-TWAs. The simulated results reveal that gyro-TWAs are the most susceptible to the fundamental-harmonic TE11 competing mode, regardless of the operating scheme, and that the mode-selective circuit can provide an attenuation of more than 20 dB to suppress the competing modes. The amplification of the waves in a gyro-TWA depends on the lengths of the sections, and the simulated results show that the gain increases for all schemes, as the length of the lossy section or the length of the copper section increases. All schemes exhibit nearly the same saturated output powers and bandwidths; however, the saturated gain of the scheme at a high frequency multiplication ratio is less than that of the scheme at a low frequency multiplication ratio. Extensive numerical calculations of power and gain scaling are conducted for all schemes.