Results are presented for a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to allow for spin wandering. This search improves on previous HMM-based searches of Laser Interferometer Gravitational-Wave Observatory data by including the orbital period in the search template grid, and by analyzing data from the latest (third) observing run. In the frequency range searched, from 60 to 500 Hz, we find no evidence of gravitational radiation. This is the most sensitive search for Scorpius X-1 using a HMM to date. For the most sensitive subband, starting at 256.06 Hz, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=6.16×10-26, assuming the orbital inclination angle takes its electromagnetically restricted value ι=44°. The upper limits on gravitational wave strain reported here are on average a factor of ∼3 lower than in the second observing run HMM search. This is the first Scorpius X-1 HMM search with upper limits that reach below the indirect torque-balance limit for certain subbands, assuming ι=44°.