Why is suicide avoidance a perfect duty?

I've been grading undergraduate papers on Kant and euthanasia for the last few days, and in making comments, I've come to realize that there's something that I don't get about Kant's argument for the immorality of suicide. I'm far from a Kant scholar, so I might just be misunderstanding Kant's view. (Luckily, my concern hasn't gotten in the way of my grading at all.)

In the Groundwork, Kant argues that suicide is immoral because it rests on the following maxim, which cannot be universalized without contradiction: "From self-love I adopt it as a principle to shorten my life when its longer duration is likely to bring more evil than satisfaction."

Something that genuinely loves itself, Kant tells us, cannot desire its own destruction; thus, the maxim results in contradiction. Now, I think it's debatable whether something that loves itself cannot desire its own destruction, but that's not the issue I want to raise. Kant says that suicide avoidance is a perfect duty, which would mean that this maxim results in a contradiction in conception. I think it looks more like a contradiction in the will, which would render suicide avoidance an imperfect duty.

I can see why the contradiction looks like a contradiction in conception. One cannot attempt to kill oneself if one is acting out of desire to preserve oneself. There is a clear contradiction there. But what makes this issue tricky is that it looks like someone who acts out of self-love could not will their own death. Isn't Kant's prohibition on suicide from self-love a case of an imperfect duty then? One can imagine the consequence of everyone killing themselves. That's not inherently contradictory. The problem stems from the willing.

One might try to make the following counterargument: imperfect duties are those that generate fully consistent perverted worlds when their maxims are universalized, but that have maxims that cannot be willed because the perverted world results in one's ends not being met. In other words, imperfect duties come about when there's a breach in a hypothetical imperative. The contradiction in the self-love maxim does not necessarily come about from a person's ends not being satisfied. But I think this is wrong. Self-love, Kant tells us, impels the improvement of life. It looks like the contradiction occurs because death ceases all improvement in life, thus one's ends are not being met.

Moreover, if we don't interpret "from self-love" as making a claim about hypothetical ends, then the maxim Kant offers does not correspond to the traditional "In situation X, I will do Y in order to achieve Z" template. Normally, if a maxim is contradictory simply in virtue of the "in situation X, I will do Y" portion (as maxims condoning lying or promise-breaking are), then it forms a perfect duty. If this is not the case, but the maxim becomes contradictory when Z is taken into account (in other words, the perverted world is consistent but does not achieve the ends of the hypothetical imperative), then the maxim forms the basis of an imperfect duty. "From self-love" seems to fit squarely into variable slot Z. If we insist that it does not but that it still generates the contradiction, then we give up on the standard maxim template, and we have to tell some sort of story about what sort of work "from self-love" is doing and why it's permissible to include in our maxim.

There is one other unique aspect of this maxim that may be relevant. It results in contradiction whether universalized or not. However, I don't know if this influences the perfection or imperfection of our duty, nor do I know why it should.