UW is tough that way - you’re correct that changing into impacted majors can be tough, especially CS. (This thread, and the Seattle Times article within, may be useful How to get into University of Washington’s capacity-constrained majors [GetUWMajor]).
It sounds as if you don’t really want a pure-CS major enough to attempt direct-admit to the major, but being shut out of the major sounds bad too. That may be enough to rule out UW, but before you give up on it, you may want to consider a few alternatives. My CogSci-curious kid was interested in both the Informatics major and the Human-Centered Design & Engineering major. Both are impacted but with your record, you could probably get the departmental admission you need if you’re sufficiently comfortable with the flexibility one of these majors would give you. It does seem as you may have other options that will give you enough aid and give you more freedom to explore majors, but it doesn’t hurt to apply to UW with the best-chosen major possible, in case it does end up being one of your top choices in the final analysis.
HCDE is very project-based and hands-on - perhaps the closest thing to a program like Olin that’s offered at a large university. Olin itself probably isn’t your jam but could be worth a look in case. Another interesting major could be the Engineering Psychology program at Tufts (Offered through A&S as Engineering Psych and through Engineering as Human Factors Engineering) in addition to the Cognitive & Brain Sciences major that was already mentioned upthread.
The important question is whether schools like Tufts and Northeastern and Rochester and etc. etc. etc. would give you enough aid, so run those NPC’s and let us know whether there are affordable possibilities in this “tier” of schools, or no.