For grad school here - you can go to name your directional like N Illinois, have a solid job and go to Harvard.
My College of Charleston daughter is in a two year ‘job’ program. If she takes the GMAT and crushed it, along with her top grades and solid work background this next two years, she could (doesn’t mean she would) get into any MBA program in the country. That’s not her pursuit but just noting it wouldn’t be shocking. Her degree was in social science. Her industry is education.
Harvard’s MBA class if 930 is represented by 269 colleges. Think about that …not sure if I could even name 269 colleges.
You are correct - work experience will impact grad admissions. Colleges don’t place. Like my kids, yours will have to hustle. Cornell until recently posted the how did they find the job and overwhelmingly it was company websites and social - likely indeed and LinkedIn. Comparatively, far less percentage wise found their jobs via the school.
I wish there was an assurance for you.
But no matter what anyone will say - there isn’t - even from the creme de la creme. 3 countries is great - but so is SUNY Oswego with a marketing job at Corning or management development job at Wegman’s (grocery store chain).
I wish you luck in finding what you seek.