I’m afraid that I can’t give too much insight into your admissions chances as the product of the British educational system; but I can give you some links (and you may be aware of them already) that can provide some data for you – how you interpret the data is of course up to you.
First, the Data Digest, here, https://www.purdue.edu/datadigest/ , provides interactive information under the heading “Applications, Admits, and Matriculations” that can be modified based on your College (“Engineering”), student level (“Undergraduate”), and residency (“Foreign”). The “New First-Time Beginner Profile” may also have some useful information.
Second, the Common Data Set, which has a link here, https://www.purdue.edu/oirae/resources.html , tells you under Part C7 what admissions factors Purdue considers as “very important,” “important,” “considered,” and “not considered”. To the extent that you can influence any of the relevant factors at this point (such as (re)taking the SAT or ACT after a test preparation course), I don’t know.
In terms of getting admitted to Exploratory Studies and later transferring to the COE, my first thought is that if this is a really easy way to get a back-door entrance into COE, then more people would have done it (i.e., it’s too good to be true). But I confess ignorance on that point. You may want to speak to someone at COE to find out whether you have to formally apply to COE from Exploratory Studies (I confess ignorance on that point as well), and, if so, what the success rates are for those transfer applications.
Have you considered applying to other universities in the U.S. to study Aeronautical/Astronautical Engineering? I think that Virginia Polytechnic Institute & State University (i.e., Virginia Tech) in Blacksburg, the University of Colorado in Boulder, and the University of Maryland in College Park are well-regarded in that area; and you may have a better chance of admission to one of those schools, as a back-up plan.
Good luck!