Guys - my own personal experience was that waiting til you have attending income (which should be MUCH better than even fellow-with-moonlighting income) will look much better in the eyes of the refinancing company. Your income-to-debt ratio is better, simply put.
@castafari: If I read that right, SoFi offered to take you from 6.8% to 5.8%? Fu*k that noise - that sucks. Just keep making payments so you get in the habit of it, and wait the 5 months you have left until you have attending $$$ before you refinance. Like I said - I went from 5.8 to <2. (Full disclosure: wife is an attending physician as well)
@chocomorsel: I refi'ed in September 2015, which would have been about 1 month into working as an attending. I have no idea on the particulars about whether you can refi again.
Take your time to do due diligence on this - there are probably like 8 or 10 different places that will refinance with competitive rates. I used Earnest, which worked well for me. I elected to take a variable rate, which works for me since I'm trying to clobber debt early with the lowest possible interest rate, but other companies might offer better/different perks that work better for your individual situation.
Look at anything on The Google about this topic and you'll find options - I just found
www.magnifymoney.com - which lists almost 20 different refi companies that offer different options. Search them out, and see what works. But if you have attending money and are still paying 6.8%, my humble opinion is you are overpaying, given the refi options.