I explored flying a bike with United about 2 years ago and spoke with their customer service team on the phone about clarification on their policy. Because as you said, 62 linear inches is impossible with a non-folding bike and 700c wheels. What I was told (summarizing) was the following:
$200 + $200 for the overweight/oversize fee (each way) if I couldn't meet the size requirement.
Ironically I met a buddy in Vegas last week (who flew United with his bike) and he was well over the 62" requirements and was only charged the $150/each way fee (domestic bike charge). We both agreed that the prospects of a round trip without incident was a fluke and not the norm.