But this is mostly just for convenience and because I feel like they might be a touch more motivated to help me find something if they are also going to be managing it...but this might not be true. 

Should the properties be valued closer to market value or am I essentially paying a “convenience” premium because the portfolio has already been built?

The MF is the best option for you but then there is still a need for spending time property managing which is not always convenient. 

It's a much higher gamble here.

If you were to try to sell that property tomorrow, you'd basically lose money.If you want to gamble for the appreciation, thats one thing.

If you are outside those areas you are taking a bigger gamble.

Since the property itself is indeed in need of a full rehab, 203(k) just seemed to be the perfect option since it allows me to roll everything into 1 convenient loan (as long as everything is within the loan limits).

Owning in FL is a gamble for hurricanes no matter what, so you might as well put a little money each year into insurance in case a hurricane does hit.

Very convenient location with plenty of amenities.

At the end of the day, an investment is nothing more than a gamble.