Abolishing the Senate is out of a question, but I think there may be an easier way to make it more representative. The Constitution requires the Senate to give equal representation to the states, but it also allows it to set its own rules and procedures. The filibuster fits under this latter requirement; whatever arguments Tom Geoghegan and Kevin Drum muster for its unconstitutionality are going to fall flat in federal courts that abide by the political question doctrine. More to the point, the filibuster can actually be helpful in assuring equal representation of voters. As Ben Eidelson showed in Slate a few weeks ago, filibusters composed mainly of Senators from big states can represent a majority of the country. Given a binary choice, I'd still prefer to abolish the filibuster outright, but this suggests a third way: a rules fix for the Senate's disproportionality.
Suppose that to close debate in the Senate, a cloture vote were required that needed not a majority or a supermajority of members, but a vote of Senators representing the majority of the country in order to pass. Each senator receives votes equal to the population of their state as of the most recent Census estimate; Barbara Boxer and Dianne Feinstein, for instance, would each get 37 million votes. If more than 300 million votes are cast for closing debate, then a final vote on the bill is held. Assuming that big-state senators wielded this power like Republicans currently wield the filibuster, the result would be that no bill would get passed without the support of Senators representing the majority of the country.
I suppose this could be unconstitutional–whatever that means independent of the whims of Anthony Kennedy–but I cannot imagine a court overturning it, the same way I cannot imagine a court challenging the filibuster. The bigger problem would be getting 51 votes to change the Senate rules and implement this. Given as only 17 states* would gain influence under a pure form of this system, you'd be 17 votes short of a majority even if every Senator from one of those states voted for the change. More viable would be a compromise that still allowed for variation, but gives disproportionate influence to enough mid-sized states to win 51 votes. While far from perfect, even a compromised rules fix would be a marked improvement over the current system, and a far more viable method of change than constitutional amendment.
*This is worth explaining further. Currently, the vote share of a given senator is 1/100. Under this system it would be their home state's population over twice the US population. Currently, the state population resulting in a 1/100 vote share under this system is 6,175,440. Only 17 states exceed this and thus would gain under this system, meaning only 34 Senators would be inclined to support the change. 51-34=17, so another 17 Senators, representing at least nine more states, would be needed to effect this change.