Hey JUrbina. Not an admissions consultant, but thought I'd weigh in a bit as a prospective student applying this year, in case it's helpful. I've visited Kellogg and Haas (and will be applying) and for a while strongly considered Wharton (but didn't visit and decided not to apply). Didn't look too closely at MIT but have a friend that graduated this year. Booth I think I took a closer look originally than MIT, but also decided not to apply or visit (but because of my friend feel like I slightly have more of a feel for MIT than Booth).
One thing that could be helpful is to share your reasons for getting an MBA and what you want to do after. Not sure if you want to do something that involves your engineering background. Some of the thoughts I'm sharing below might become irrelevant or less true (or truer) depending on that. Some of my thoughts might be influenced by assuming you may lean towards the engineering, quant, schools.
The part I might be able to add the most value to is with Haas. I know you already say it's a bit of an oddball, so if this info below is stuff you know and why you called it that please disregard. First off it's way-way smaller than the other schools you mentioned (500 students to the Booth's 1,200 as the next closest) and that impacts the experience and feel. I also think it plays out in the number and variety of courses offered and potentially the depth that class topics might go into (depending on the subject/focus). They just aren't going to have as many classes and professors as Wharton or Harvard being 1/3 as small. I am applying to relatively smaller schools except for Kellogg and what I love about Kellogg is the wide course selection and ability to really feel I could get a rich business academic experience and could choose to go deep into a number of topics there. Haas I sometimes have wished they had a little bit more of what I want to study from looking over the class schedules and website (not to where I won't get an excellent education and business management foundation, but more on how specialized I can get). I like it for other reasons though- the rich personal experience in my opinion with the smaller school, access to Silicon Valley and a lot of hands-on opportunities to learn what I want to, that I could be happy with an excellent general management curriculum. Note: my interests aren't obscure but also not super common. When you're talking entrepreneurship classes at Haas there are obviously a lot of options, but for depth in a variety of topics I'm talking relative to schools like Kellogg and Wharton from my research. Just from what you shared about Wharton and MIT not sure I've gotten those same vibes from Haas (except for the entrepreneurship part at MIT). Primarily it was Wharton's strong presence in all other aspects (I took that to mean a lot of classes and excellence in a wide variety of fields) and then the heavy modeling, engineering at MIT (from my research and visit Haas has struck me more on the opposite side of the spectrum from engineering, finance, quant, etc.) where I saw the most difference.
Hope that is helpful and was not meant to try and convince you not to apply to Haas. You may have other reasons for loving Haas and someone (especially a current student or alum) might be able to come along and refute some of this. If the smaller school and collaborative atmosphere appeals to you (you might be considering two very different experiences and want to wait until you know where you're accepted to decide between them), I found a lot of similarities between Haas and Tuck. Booth seems way more aligned with Wharton and MIT and then Kellogg (to a degree) with the larger size, the number of classes and excellent education in so many different focuses, more "quant" like MIT and Wharton, etc. Plus it's in Chicago like Kellogg (and despite some different vibes and fit people often apply to both).
I saw you included a few more schools on your profile including Stern and Darden. Because of some geographical preferences, I didn't look closely into them, but it brought another school to mind only if it's helpful. Since you're also looking at Darden it made me think that you should take a look at Ross (less because they are similar, but more because you're looking at schools similar to its ranking). I found a lot of similarities to Kellogg at Ross in terms of the vibe and feel. Also despite it being smaller I thought it seemed to have a lot of excellent options for class and academics in a variety of fields like at Kellogg and Wharton. It could also maybe be some middle ground between a school like Haas and a school like Wharton in terms of size, options.
You might have thought a lot about your strategy for applying (such as saving some lower ranked schools for Round 2), but one other thought that came to mind about your schools was they're 3 of the top 6 schools (4 if you include Booth). The admissions consultants can better comment on your chances, but I've seen admissions to top schools sometimes be such a crap shoot even with very high stats. Had a lot of friends apply and sometimes admissions seems to make no sense. But since you were asking for feedback about the schools you picked their selectivity was the only other major thing that struck me and where it could be helpful to think about schools like Darden, Stern, and Ross. Again you might have a strategy for keeping some schools for Round 2 (and you did include other schools on your profile), so apologies if you've thought of all of this.
Finally to your question on whether three schools you mentioned as top choices make sense, I think there are always tons of different reasons why people like schools and the ones you listed make sense to me as a fellow applicant and are at a similar level to the reasons that I had a gut feeling for my top schools originally. I've seen/heard varying degrees of things like collaboration, methods, emphasis on finance/quant, etc. at those three but it doesn't strike me as odd for those three to be included together (vs. say including Wharton with a Haas or a Tuck).
Hope this was helpful and not recapping things you've already thought about. In case it could be helpful in your research and you don't already know about them, Poets and Quants, Veritas Prep, Clear Admit,
MBA Mission are all websites where the school profiles helped me discover, narrow down, and do deeper research if you are looking for handy ways to explore schools that people here suggest.