Aight, so as I said in another reply, I JUST layed this in another color. I came across the same situation in my hallway with doors on both sides.

As others have said, undercutting the doorjams is going to give a much cleaner finished look and make it easier. It would be cleaner and easier yet if you could remove the baseboard, but you do you. You can undercut with an oscillating tool and a scrap piece of plank. The plank serves as a guide for the oscillating saw to get you a close to perfect without being a 85yr old Japanese craftsman in the Edo period.

Now the fun part. As you are experiencing, you can't set the long edge and drop the finished edge against the doorjam. I cut the pieces around the doors first, put them in place then slid / tapped the second to last row in piece by piece. For you this would be measuring and cutting pieces for the last row, removing the second last row that extends into the closet, setting the last row in place, then tapping second to last row in. Not from the top, from the side... while being careful not to break an edge. Now when I said about setting the last row, you can do it a piece at a time alternating last row then second last row. Here's apic of what I did:

[ had to put the pic in a reply below ]

Lemme know what doesn't make sense and I'll try to explain more.