I'm trying to understand the "legal fiction" wherein we declare any chometz we have as ownerless like the dust of the earth. Is this halachically acceptable? How can a person declare something in his possession, possibly locked up in his house to be ownerless?
The original practice of Bittul (Pesachim 6b) was for after one searched for and found all Chametz, and essentially we are left a concern that maybe he will find something small on Pesach that he missed, essentially saying "that too is as irrelevant as dust." It does not help for a locked away closet full of Chametz.
That being said, as a Torah matter, it would help if he was sincere (see Shulchan Aruch HaRav OC 431:2). If someone specifically locks it up in his property, that is quite a sign of insincerity - and no one suggests this is a real way out of the problem, but say a person leaves it out on his front lawn where it is easily taken. Then even though you may not possess it, the fact that it is on your property is not a problem - as a Torah matter. The Chachamim don't allow that (because you might forget and eat it or because you might not be sincere and just hope people won't take it).
Once Jews started having a serious inventory of Chametz, the practice of selling it was introduced. This works around the locked closet problem, and to some degree the sincerity issue as at least the owner stands to get paid market value for the items. However, the pro-forma nature of the sale has had many objections that even that practice isn't sincere and thus not valid.
First if it is a "legal fiction" then you are in fact transgressing biblical and Rabbinical commandments regarding possessing Hametz over the course of Pesach.
First you are referring to the Bitul Hametz that we all recite. However it is important to note that the formula of that specifically says,
"Any leavened food or leavening in my possession that I have not seen and have not destroyed is hereby considered null and and like the dust of the earth."(Yalkut Yosef 344:3)
It therefore does not cover any Hametz that you have seen, know full well where it is, and have no intention of destroying.
Now regarding deciding to truly make your Hametz ownerless many poskim(halakhic decisors) say that you cannot reclaim it after Pesach(as that would cast doubt upon the initial declaration). The Yalkut Yosef however brings a slightly more lenient approach and says: In practice, if there are witnesses that the owner sincerely declared his Hametz as hefker(ownerless) and it is clear that he did not do this as a way to sidestep the halakha requiring him to destroy his hametz, he may then reclaim the Hametz after Pesach if it would cause him a significant loss otherwise. It is best, in such a case, that after reclaiming the Hametz he mix it with other Hametz[that he purchased after Peasach] so that the reclaimed Hametz is a minority of the mixture and unrecognizable in the mixture. (Yalkut Yosef 448:4)
Likewise you seem to believe that the sale of Hametz is also a legal fiction. In truth for many years it was and many many major halakhic authorities spoke out against the practice. Even today there are many people who do not rely upon the sale of Hametz. However, for those that do, they have what to rely upon so long as the sale is not a legal fiction, either to them or to the one buying the Hametz. Here is an article that goes in depth in to the various halakhot that are involved in sales of hametz by any reliable agent of sale today. By Rabbi Peretz Moncharsh who's bio can be found here.
When making something ownerless it is just that ownerless. In Halacha, to take possession of something you must pick it up or otherwise possess it. If you were to move something that has chametz, you would be regaining your ownership of it. If it was sold, you wouldn't be since it has a new owner already.