Let $f_i$ be chopstick $i$'s final length. The removed length is $\sum_i(a_i-f_i)$, so minimizing removal means making the final lengths as large as possible.

Each chopstick can be shortened at most once. Its current length is therefore either its original length or its final length.

View chopsticks as vertices and sushi as edges. First eat every edge whose endpoints have equal original lengths. These operations change nothing, so doing them immediately is safe.

We can now focus on unequal-original edges. They determine which chopsticks must be shortened and when final lengths must become equal.