I second this. I would strongly encourage re-considering your opinion on a gap year. There are many advantages and few disadvantages to a gap year. If you find even a mediocre job, you will not be burdening your parents.
$10/ hour x 45 hours/week = ~$1300/ month after state taxes (assuming a nearly full federal income tax return).
If you live at home, you will have over $13,000 to work with to help your parents pay for food, your loans, even rent.
This would allow you to apply after college. This means:
1) Longer and more meaningful ECs (many other applicants are applying in between their 3rd and 4th year too! But you just won't have that fourth year).
2) More time to spend on your interviews and app (your third year would likely be horrible with 20 credits and having to cope with the stress of an app cycle).
3)
Time to spend with your family and recoup from the burnout that is highly probable from a 3 year undergrad at a good school. ( This is in my opinion the most important!!) After I did an engineering/premed undergrad, taking some time to myself was absolutely one of the best choices I made during undergrad.
4) Getting some work experience to talk about during interviews (and it is a good life experience if you haven't had to already).
5) If you can get a job doing something academic (like research), you can not only get paid but work towards publications and presentations that will help you in the future. This is exactly what I am doing and I could have a couple pubs and a couple presentations from my gap year that are relevant to medicine... I can see these helping me in my residency search.
There are plenty small perks too. Please feel free to PM me if you have any questions at all. Best of luck!
If you really want to do undergrad in 3 years, then just apply after you graduate. You will have a year "off" of secondaries, interviews and what not but that's pretty normal, you could also work full time in this year if you need the money.
I don't know your financial situation but I have many friends who came from backgrounds where their family could provide no assistance and through a mixture of working and loans they were fully able to support themselves.
They weren't particularly smart with their money either, so I imagine that if you planned and handled things well you could do this well.
Its not that difficult to work 3 days a week if you are smart with your time.
EDIT: I notice you set you didn't want to take a gap year, but maybe I'm missing something. What is stopping you from working full time in this gap year and not burdening your parents? Seriously, start working in a decent restaurant part time early, and in a year or so try to wait tables. Easy, flexible and good money.