Inverted rows (trigger warning: also called fat man pull-ups) are extremely underrated. But over the past couple years, they've become my favorite rowing exercise, especially for those with back pain. They allow you to attack the upper back without putting pressure on the lower back. They also help to activate and strengthen the glutes, which are generally underactive in back pain sufferers.
If you have suspension straps – TRX, Blast Straps, rings, etc. – they're also very shoulder friendly because they allow you to rotate your hands through a natural range of motion from pronated to supinated, which strengthens the rotator cuff. If you don't have straps, you can use a bar in a power rack or Smith machine.
Elevating the feet on a bench so that the torso is parallel to the floor increases difficulty. Lying plates across the chest or wearing a weight vest are further progressions. Once you've mastered regular inverted rows, try using "1.5" reps. Row up, come halfway down, row up again, then come all the way down. That's 1 rep.
These help ensure that your form stays tight and allow you to concentrate on retracting your scapulae and getting a good contraction on every rep. Want to ramp it up even more? Try this:
Set up as you normally would for an inverted row except hold only one strap. Extend the other arm straight up toward the ceiling and place your feet a little wider than normal for a more stable base.
To do these successfully requires extreme total body stiffness, so contract everything – glutes, core, lats, grip, the other arm – literally everything. When you're ready, row yourself up and reach the non-working arm straight towards the ceiling.
Your torso will want to rotate slightly towards the side of the working arm, which is fine as it allows you to achieve a greater range of motion on the row. Just don't allow your hips to sag. Lower yourself under control and repeat.
Each rep should be performed under control such that you could pause each rep at the point of contraction if need be. You can also start with your feet on the floor if elevating them is too challenging at first.
While this is ostensibly a back exercise, it's really a total body exercise because every muscle from head to toe must fire to stay tight or you simply won't be able to do it.