My vague recollection is that this is very close to the date that I took the SAT when I was applying to MIT as an international student from Canada. This worked fine.
Is that in Canadian dollars or US dollars? Meeting this budget even in US dollars is uncertain. You need to run the NPCs at the private universities in the US. Reaching this point at the public universities seems unlikely to me.
One daughter was accepted to U. of Colorado Boulder many years ago as an out of state student and was offered merit aid. Even with merit aid it still would have cost about $40,000 per year (in US dollars, not including travel) and I would expect costs to have gone up since then. Given your stats it would not surprise me if you also get some merit aid, quite possibly a similar amount to what my daughter was offered, although I am unsure whether an international student is treated the same as an out-of-state domestic student.
Have you run the NPCs for MIT and Stanford? They of course are not even remotely close to your budget unless you qualify for quite a bit of need based financial aid.
Being a permanent resident of course puts you on the same level as a Canadian citizen. This will help a lot at universities in Canada and will indeed allow universities in Canada to be affordable.
I think that you might be underestimating the quality of the universities in Canada. Canadian universities are in general very good. Of course Toronto and UBC are among the best in Canada, although there are a lot of very good universities in Canada.
These are very good universities. Calgary is also very good. I think that aerospace engineering is a minor there rather than a major, but I doubt that this makes much difference in terms of either what classes you take or your chances to get a job after graduation. Being a Canadian permanent resident I would expect these to meet your budget, even in Canadian dollars.
I would expect your chances at Toronto and UBC to be very good. Note the cost of housing in both locations.
I do know multiple students who got a bachelor’s degree in Canada and then got (or are currently getting) a graduate degree in the US. This includes one student who got a master’s and PhD at Princeton and two students who got master’s degrees at Stanford. This also includes one daughter who is currently getting a PhD at a very good program in the US. Even the highest ranked graduate programs in the US know how strong the Canadian universities are.
One option that you might consider would be to get a bachelor’s degree in Canada and a master’s in the US. This is more likely to be affordable if you find universities that have a one year master’s program. Depending upon whether you qualify for need based aid, and how much aid you are offered when getting a bachelor’s degree, this might or might not cost less compared to just getting at least some bachelor’s degrees in the US.
One issue to consider is that getting a university degree in the USA does not allow you to stay in the US after graduation. You will almost certainly be required to return to your home country (whether Canada or the UK) after graduation.
Also, at least in my experience Canadian employers seem to prefer to hire graduates from the excellent universities in Canada rather than from universities in the US, even when considering highly ranked schools such as MIT and Stanford.
Also, getting a student visa to study in the US has been a bit uncertain recently. I do not know whether this has settled down and become predictable again. Coming from the UK and Canada does seem like it might (or might not?) help compared to coming from some other countries, although again I find this hard to predict. Way back when I did it getting a student visa coming from Canada seemed to be straightforward, but whether this has changed might be worth looking into. Most certainly, when applying for a student visa, do not tell them that you intend to stay in the US after graduation. The intention to stay in the US after graduation can be grounds to refuse to give you a student visa.
And I do wonder whether being in the US for four years, and therefore not in Canada, will have any impact on your permanent residence in Canada.
Finally, since your entire post starts with “chance me”, I guess that I will do this. I think that acceptance to UC Boulder is likely, but affordability is uncertain and I do not see the point in spending more to go there compared to options in Canada. I expect that admissions to Purdue is also likely, and have no idea whether it will be affordable. I think that GT, UT Austin, Stanford, and MIT are all reaches. You are a competitive applicant for any of them, but so are most of the other international applicants.