soapy water and no tire lever.

Once you get to the last few inches of tire to go on, stand the wheel up and turn this section away from you. Using the palms of your hands, pull the tire over the rim towards you. Use one hand and then the other not letting go so you can keep whatever progress you've made.

Continental designs to to upper margins of ETRTO for safety reasons. This means their tires can be particularly difficult to mount.