Your terms are going to be better right now because its owner occupied.

You won't be able to get a dscr loan if you're going to owner occupy it. 

I plan to start a deep dive into off-market deals in the next couple of months, aiming to occupy the property by July of next year.

The credit score is around 720, and the property is owner-occupied, which might simplify the process.

Management: Only when tenant occupied, the greater of: 5% of gross rent per month per unit or $100 per month per unit.B.

This is true in Ohio as to residential owner occupied but not commercial.

I am trying to house hack a 4 unit multifamily (FHA 3.5% down, owner-occupied, rent other rooms) in San Francisco or Los Angeles and could use a bit of help starting out!

There are also probably a few that at some point will be buyout candidates for multifamily investors, but that is not easy, and is probably now 5 years or more on the horizon.There are also just so many things that can go sideways with tenant occupied condos. 

@Daniel Afonso You can buy properties with as little as 3.5-5% down of the purchase price if you are planning to owner occupy the property.

For example, if the loan is strictly for a business purpose (non owner occupied) or temporary financing (e.g. construction loan), referral fees are allowed.