Not going to happen if you REALLY want things to stay aligned across the spreads unless you edit the text. I say that because I count a three-line space in a four-column layout. You also want to get rid of the very last paragraph return a the end o f the story before you start messing around.
What might sort of work would be to set the vertical justification on the right-hand frame to Justify in the frame options, and also check the Balance Columns box. The frame should then have two columns that have text top to bottom, but the line spacing will no longer match the frame on the left.
Personally, I don't see what is wrong with the end of the spread.
A couple things, you have a blank paragraph at the end of the 4th frame. Anything you try is going to attempt to act upon it as well. Second, you have 3 lines blank (after removing the blank paragraph) in the 4th column. 2 frames of two columns. Adjusting both frames will never work out.
You can highlight the text and adjust tracking. Use small amounts. In the screen shot, I am using 6 ems.
But this would be pretty fiddly throughout a publication. Same with manually kerning each spread.
You can select the frames and in the Frame Options, choose to use Justify in the Vertical Justification section. That will probably be the easiest but it can bite you at times if you forget. It can affect lining up from side to side of the spread as far as leading goes.
Take care, Mike
At the bottom you can see the end of story or paragraph marker. At least that's what I think the blue thing is in the screen shot. Eyes are failing, though.
By the way, I evidently edited out the fact that adjusting the tracking and or kerning is best in that it doesn't affect leading. Judicious editing, if possible, also helps.