@Aaron C.
You have a few options, you can do either of the two options you mentioned such as discounting the existing price, or raising rents if you believe the market will tolerate the increase. I generally stay at or just below market to try to lock in quality tenants for longer periods of time.
If you find a property that takes FHA, but is distressed, you do have an option with the FHA 203k loan that you can use to purchase and fix it up, this does require using certified contractors pre-approved by the lending bank (generally more expensive than contracting out yourself or DIY).
If you do happen to find a deal and negotiate it to take FHA with 203k repairs, the numbers may still be able to work in your favor. You do have the other option of a hard money lender once you find a deal and then conventional refinance upon completion of repairs and seasoning requirements.
Finding partners to get in on the deal (remember you can receive a gift to help with down payment with an FHA loan from immediate family) is another option. I don't recommend trying to circumvent any FHA underwriting rules, but if you can get creative with financing while making your initial or subsequent primary residence house hacking investments work for you, more power to you!