"As a result, a new plan would call for the House to pass the Senate bill and send it to Obama. The Senate would then use budget reconciliation rules to make several changes demanded by House Democrats. Those rules prohibit filibusters."
What reconciliation rules they are I don't know.
Was this procedure hard to figure out?
Was the plan hard to figure out for the media and other commentators? Probably, because they don't have access to the House rules people, nor do they think about procedural maneuvers all day.
In retrospect, passing two bills was a very elegant solution. By passing the Senate version straight up, they guarantee that at least some version of victory is achieved without having to deal with the 59 seat issue. Then sending an amendment package back to the Senate with only carefully chosen amendments that allow the reconciliation maneuver gives it a decent shot despite the loss of the supermajority. Had they tried to pass one bill that combined the original and the amendments, the filibuster could have killed it.
The reason reconciliation was set up was so that the financial numbers could be tweaked with minimum fuss on bills whose policies were already voted for by the Senate.