I reckon for this challenge, steepish climbs would be the best bet. Very steep climbs would probably kill your legs, but maybe something like a steady 10%. My thinking is that you would be going so slowly that nearly all of your power would be used in lifting you and the bike through so many metres, and hardly any lost to air resistance. Also, you would be able to freewheel all the way back down to recover between efforts ...
The kind of thing I am thinking of is the Otley Chevin climb which is almost exactly 10% all the way up for ~1.6 km, gaining 160 m. You would have to do it 56 times, but you would 'only' have to pedal for about 90 kms and would cover 180 kms in total.