I just went through a difficult tire-rim fit, where the tire wouldn't fully climb the rim. The tire was Continental, and the particular rim caused trouble with other tires, too. In the past, I might have improved the seating, but the hiccups in riding still remained. This time, I had a couple of days before the bike's first use with that tire, so I pushed through to a full solution. With this, I can report how different methods to cope with the challenge worked.

Improving the tire's seating by hand while gradually pumping did nothing. Using tire levers or the tire seater I suggested, on their own, allowed the poor seating to spread a bit, reducing hiccups in riding, but did not eliminate them. High pressure and pouring talc between the bead and rim did nothing on their own. What finally worked was generously spreading soapy water with a brush between the tire and rim. At high pressure, the tire climbed the rim with a pop, distributing itself very evenly.