Some advices regarding the first research paper
Ask your professor to introduce you to a suitable expert.

If some of your professors think that your work is of substantial quality and probably novel, then they are surely fine with introducing you to some suitable researchers in the field. Note that, for example, a postdoc in the respective field may suffice. They should be willing to give your work the "badge" that in their oppinion, your work seems to have potential by writing that to the suitable researcher themselves. This should get rid of the problem that you describe in your second-last sentence: 

"But unfortunately I don't know anyone such and I see no point in assuming that even if my work is significant, they would give time to read it without dismissing it beforehand as a work of some crank."

Note that an experienced academic in the respective field can add a lot of value to your paper, including improving the accessibility and providing a more comprehensive literature survey.