Take your wheels to the store and fit both tires on when shopping for Continental`s touring tire models. Watch & see why.
You check that your rim is round? +/- 1mm from 622 will not give you the issue you are having. Have you checked the bead is where it should be on the opposing side when mounting the tire? the inner tube will not be destroyed if you know what you are doing. I notice your not rolling the bead over in the correct spot when mounting this as well…