See this article which sites Likutei Maharich that explains why for Selichot Yamim Nora'im they added Ashrei and other items
In summary, he says that Ashrei is like psukei Dezimra. The Selichot with the 13 Middot is like Shemoneh Esreh, and at the end of Selichot, they say Tachanun and end with Kaddish, similar to the main content of a Shacharit service.
So, while I haven't yet found a source that specifically allows saying fast day Selichot before Shacharit, (see my comment above that implies that it looks like it's fine to do this. but I can't affirm it.) I'm inferring from this article that one would have to follow the format that is used during the Elul - Erev Yom Kippur Selichot, i.e. Ashrei, etc. I think the reasoning is general to all Selichot, not just this period.
It's moreso that the common format of fast day Selichot occuring just prior to or in mid-Tachanun, has already taken care of the need for Ashrei. Your question, of course could be asked in reverse, namely, why aren't the Ellul Selichot said in the middle of Shacharit, instead?