If UIUC recommends discrete for potential CS transfers you should take it, competition is fierce for the few transfer slots there are in CS. And you are correct that Interdepartment/school transfers and Illinois community college transfers have priority over an international student.
I know less about the CS + Math major, but it also sounds highly competitive (do you meet all the criteria?):
Transfer applicants who have completed more than 6 semesters or 80 hours of coursework are subject to an additional review. Priority is given to students who can complete degree requirements within a total of ten semesters in college (not counting summer sessions). A grade point average of 3.50 or higher (A=4.00) is required for admission to Mathematics & Computer Science. However, a minimum grade of A- is required
on each Computer Science and Mathematics course taken. Applicants are considered on a space available basis.
You should consider UIUC a reach…is it affordable? If you are certain you want to transfer to the US to study CS, you will need to apply to other schools as well.