Your 2km speed is really good relative to your 100m speed (2:06 vs. 2:00). So if I were you, I would work on speed for the 100m for a while. I would proceed differently if 2km is what I was really all about, so write back if that is what you really want.
The big deal about the tempo trainer is that after you basically learn to swim pretty efficiently at low speeds, the tempo trainer helps to train your nervous system to maintain that efficiency at progressively higher tempos (and therefore faster speeds). So since you told us SPL is 22 (in a 25 meter pool?) I am thinking your current tempo is roughly 120/88 (2 minutes is 120 seconds, 4 x 25m = 100m so 4 x 22 = 88) = 1.36. So first off fool around in the 1.3 to 1.4 zone and see if you can mimic your current 2:00 22spl while adhering to a set speed on the beeper. Once you have quantified what you are currently doing, then it will be time to start speeding up. So for argumentís sake let's say you currently always swim at 1.32. Odds are you would feel uncoordinated at 1.2 and darn near panicky at 1.0. You might think your goal is to swim 22 spl at 1.2 and eventually 1.0. That is not correct. Your goal is that your SPL slips in a graceful manner. When I go from 1.3 to 1.0 my spl goes up (gets worse) by 10 percent, but since my tempo has gone up by 30 percent I am still getting a good (20 percent) speed increase. That is what you want. How to get there? In a nutshell, practice the fastest speed where you don't fall apart. So if you are swimming 1.32= 22 spl then you are allowed to slip to 23 spl at 1.16 and slip to 24 at 1.0. If you can already do that then you can already swim a 100m @ 1:36, but that is not what you report. So this is what I suspect; as you lower the tempo trainer 1.32, 1.28, 1.24, 1.20 you see 22, 22, 23, and 26. You see what I did? At 22, 23 you are still holding your efficiency. At 26 your efficiency is so bad that your speed actually went down even though you are trying harder. The numbers are fictional, but you really will have a non-graceful raise in your spl at some tempo. The fiction is that I made up the tempo instead of you finding it experimentally. But you can now see HOW the tempo trainer lets you find it experimentally. So find it, note it, and mostly stay away from it. In my example you will swim a lot at 1.24 (still pretty close to 22 spl). After a few weeks try the 1.2 again and if it is now 23, start training at that speed and see what happens at 1.16 and 1.12.
The power of the tempo trainer is that it lets you quantify your faster workout, but also know where your form breaks down and avoid practicing with crummy form.