Of course, with the way things are now, the Senate version basically has to win in order for the system to work. That seems terribly unfair to the House. There has to be a better way. I would say the Senate should get rid of the need for a 3/5ths majority vote to end debate, but I don't actually believe that, because it is a reasonably valuable way to protect minority rights (as I argued 5 years ago when they were considering getting rid of it WRT judicial appointments).
The only way I can imagine to make it harder to stop passage of bills but also retain minority rights would be to force them to filibuster the bill the old fashioned way, by giving long speeches. I think the Republicans would love this, though. They would have started talking in January and they wouldn't have stopped yet.