I believe the standard term for what you are talking about would be "preliminary results," and there is indeed a good place for work of this sort in the scientific literature.
The test for whether something is publishable is not whether it conforms to the idealized scientific method. The test is instead whether it makes a meaningful contribution to the pursuit of knowledge. For work that can be (usually retrospectively) fit onto the idealized scientific method, this test is fairly easy to pass.
There is also, however, a place for many various types of preliminary work, such as:
- clearly formulating a problem and explaining why it is interesting or important to solve
- developing a method for attacking an unsolved problem of interest
- reporting a study that shows suggestive results, even though these are not definitive, this helping to motivate a more conclusive study.
All of these can be valuable in a number of ways, and all of them demonstrate incremental progress towards one's goal. The question of whether a particular such piece of work is publishable then boils down to whether the partial result is significant enough to attract interest in the venue in which one proposes to present it.
For this reason, "preliminary" work is less likely to get published in a field's top venues (though it most certainly can be, if enough people care about the problem)---the bigger the problem, the more that people will likely be interested in chipping away it little fragments of it (for example, think about all the preliminary work published on hunting the Higgs boson or chasing P=NP).
There are generally also more informal venus like workshops, symposia, etc., which are quite well suited for discussion of preliminary work.
In short: if you think the partial results are interesting, then it's entirely reasonable to try to present them in the appropriate context.