Let’s be clear: Relying on H1B without a graduate degree is a bit risky. You will have 12 months of OPT on your F1 after you graduate. If your graduation coincides with an economic slump, it will be even riskier. Bottom line, you’re probably looking at getting an MS after graduation (which is a great option). Many universities support MS students financially (and waive their tuition) because they make good teaching assistants. So you’ll be looking at six years of school before you can start paying your family back. This has the added benefit that you may start at Cal Poly (cheaper by your numbers), use some F1 CPT to put research under your belt at some other university during summer, and then apply to grad school to a top school (like UW or UCSD).
No luck with SNU, KAIST, POSTECH, etc? BTW, kudos to you for being willing to jump continents in pursuit of your ambitions; that’s pretty courageous.