Because of the specificity of the speed range, which would seem to eliminate the tires as the source, I agree that a bad torque converter lock-up mechanism is a very real possibility.
This vehicle should have had its trans fluid changed at least 2 times already, so if–as I suspect–the fluid hasn’t been changed for several years, this would be a good time to take the vehicle to an independent trans shop (NOT a chain-run joint like Lee Myles, Cottman, Mr. Transmission, or AAMCO) for a fluid & filter change, and for them to check the operation of the TC lock-up mechanism.
A good trans shop will know that this vehicle requires fluid that is specific to Honda transmissions. If the OP goes to a shop that uses a generic trans fluid plus a “magic” additive to make it Honda-compliant, I strongly suggest that he should go somewhere else for service.