I recommend that you try the McGill Curl Up and the Pilates 100, or the Pilates double leg stretch. I can't say for certain that your back will like them better, but it is time to stop doing the old fashioned crunches and try a new approach. I might also recommend Planks, except that my problem with planks is that almost everyone at my gym does them with horrible form. If you can have someone watch your form and keep you honest, then Planks are a well established core exercise.
Next, a word about the biomechnics: In crunches (and other exercises), the wear and tear on your spine is proportional to the speed of the movement. So, whatever ab exercise you choose, it will be less harmful for your back if you slow down. Most people don't want to slow down their crunches because this makes them more difficult, but if you have the fortitude, I recommend slowing down. You might find that the crunch in the lower picture is impossible to do slow; this means it isn't the right exercise for you. If you can't do the movement slowly, then don't do the movement at all.
Notice that the McGill curl up and Planks are isometric, so they do not have any speed, which is why they are recommended for people with back pain. The Pilates 100, also, does not have speed, in so as far as your spine is concerned (the speed is in the arm movement).
A second bit of biomechanics: The wear and tear on your spine is proportional to the number of repetitions. This has actually be shown in studies on human cadavers and pig spines. So, I would slow down and cut the number of repetitions to around 60 total. Fewer reps, slower movement.
If you want to learn more about the spine and crunches, I recommend listening to the expert Stuart McGill on a podcast.
And lastly, the exercises mentioned about are for the purpose of functional fitness: which means training your abs so that they support your spine and improve movement. (Proximal stability for distal mobility.) On the other hand, if your goal is hypertropy (bulging abs), this is a different matter.