I think you're ahead of the game for worrying about loans at this point, so congrats.
Lets break down the loan to see how much interest is being accumulated each month. You have $184k at lets say an average of 6%. That means you will be accruing $1000 a month every month till you pay down some of the principle.
Average salary of a medical resident is ~50k for intern year or lest say $3,300 a month post taxes. Putting a third of your money towards a loan would be quite aggressive when in residency but it can be done. I did it my final year of residency but it meant that I made a lot of sacrifices. Here is my budget in residency.
I agree with other posters above that REPAYE may be your best option to start out. You can take advantage of the subsidized interest while not breaking your budget. The downside is that your debt will be compounding and building since you will not be paying enough just to cover the interest. However, I suspect you will be in this program for a short period of time. If you will be anything like the cardiology fellows at my program, they all made at least 3k a month moonlighting on the side. Many used the money to pay down their loans or save for a down payment for a house.
You mentioned that you want to pay less on your loans so that you can "balance enjoying life, pay back loan and invest." Paying down your loans with 6.8% interest is a guaranteed return. Once you're an attending you will most likely not be able to write off student debt interest anymore, so to me it makes sense to avoid investing in taxable accounts and pay down the debt. Putting money into a ROTH is a good idea though or your 401k if your program offers one.
The route I choose was to refinance my loans to half the interest rate you had. That meant that I was only building <$500 in interest a month , a value which I could spare even as an intern. Your debt is kind of in that middle ground where its no so outrageously large where you have no choice but to enter into a income based repayment plan if you choose to refinance. If you choose to refinance, just know that there are a lot of companies that are hesitant to refinance new residents.
Here are some links were I wrote about my experience
Student loan repayment guide
My budget while in residency