Is my dropper post too long?

Dropper posts are not much different when it comes to bike fitting when you think about them being at their full extension. You should reposition a seat post to such an insertion depth that the saddle's position is comfortable for you to pedal. Then, there are issues of the saddle being at its lowest position (on full suspension frames it might occasionally touch the wheel), but they are really secondary at most.

Unless you have a post that is literally integrated into the frame (and KS Lev Integra is not, it is a separate unit), you can loosen the seatpost collar and move the whole unit up and down and then re-tighten the collar. In your case, you should try sinking the seatpost deeper into the seat tube.

There are limits to how deep a seatpost can be sunk, of course. For regular seat posts, it is the curvature or butting of the seat tube, bottle bosses or other geometrical properties of the frame. For dropper posts the limiting factors are same, plus one more limit is the presence of a seatpost collar which is thicker than the rest of the outer tubing.

You should try lowering your post as low as it goes in the frame. Most likely it will stop at its own collar pressing down at the frame's seat post collar/binder. If then, at its full extension, the saddle still feels too high, you are likely to have a frame too big for you.

From this point, you can reposition the seat post as a unit a bit higher until you find the best setting for you (keep it fully extended when doing so). As you correctly noticed, even a single centimeter makes huge difference, so feel free to experiment over time. As usual, be sure to not violate the minimum insertion depth marking on the seat post (or at least 10 cm).

A new, less tall saddle perhaps?

That is possible, but it is likely to win you just a couple of mm, and your choice of saddles will be very limited.

Thicker pedals?

Maybe, but thicker pedals are also heavier and more likely to experience rock strikes. Again, you are unlikely to gain more than a couple of mm at most.

Shorter cranks would also be a "geometrical" solution, but they create new bike fit issues (e.g. knee pain) to tackle. Not to say that new cranks may cost more than a new dropper.

Is the travel of the dropper post adjustable?

The best way is to consult with the manufacturer. Some dropper posts on the market, especially newer models with travel values bigger than 150 mm, are internally adjustable; more "classic" designs, to which KS Lev is likely to belong, were not designed with that in mind.

If you are mechanically inclined, you can always try to clamp an internal shim on the post's shaft to limit its travel. Please don't cut your frame's seat tube to make it go lower!

I've found evidence of people achieving the desired effect by enforcing a new extension limit externally:

I ended up tying a wire from the seat post clamp bolt to the seat rail to limit how much it can go up. It's kinda ghetto, but works!