Qualifying for a mortgage despite massive student loan debt

[Dr. Jordan E Smith]

I'm new to the forum, just heard about it in Brandon Turner's book on rental properties and signed up today. 

I have been learning about real estate primarily through audiobooks and several real estate agents and investors I know locally. I am currently getting my real estate license and am very new to the field. 

I am interested in slowly accumulating rental properties over the next 10 years for eventual passive income (the government takes >50% of a high earned income, which of course I learned about AFTER becoming a doc. Screw that.). So I am very interested in additional passive income now. The one thing that keeps concerning me is my potential to qualify for a loan even once I've saved up a 20% downpayment. 

I'm concerned because my husband and I are both recently graduated doctors and still have a very large combined student loan debt (approx 575,000 combined - I know, it's insanity) plus car loans (about 32,000 combined) and credit card debt (about 11,000). Our credit scores are 650 and 690, and we are rapidly paying down our debt using Kiyosaki's strategy, but it is obviously going to take us a while. 

However, both of our incomes are increasing and our cost of living has significantly decreased recently due to other fortunate circumstances. We do not currently own the house we are in, but do not have to pay rent or mortgage, thankfully. We are saving 10% of our combined income (currently 80k after wretched taxes) for a downpayment on a rental property (either a single family home or a duplex) and should have a substantial amount saved in 3 years (>24,000) as well as all other debt except student loans paid off. Obviously our income will increase but I'm being conservative. We estimate our credit scores to both be >750 at this point if not higher.

I'm curious if anyone else has qualified for a house loan despite having massive student loan debt and what credit score was required, if so. 

I've also just basically put our whole financial statement out there because I'm open to suggestions on the best way to get started. Should we try to pay down the student loan debt before investing in real estate? Has anyone began investing while still in debt? Does our plan sound feasible? What suggestions do you have on our situation? 

I'm a little nervous having put all our humbling financial info out there but I'm excited to be a part of this forum and learn as much as possible! I'm 27 by the way and hoping to turn our situation around by age 36 :) 

Thanks for any help!

-Dr. Jordan Smith