Take into account the travel time, phone / video time, mistakes along with all the other economic factors.

With a household count of 250,000 to 300,000 in Memphis, that represents only 0.05% of the overall market (and maybe half of that when looking at single-family detached).To your other point, starting off with a 25% equity position is a decent position to be in with any market downturn. 

"Can I make an offer contingent upon finding a tenant to lease the space within X amount of time?

I like the idea of short/mid term rentals more then the long term...one big reason is not having to move all of his stuff...or at least being able to take my time.

People sign leases stating that they agree to no pet policies all the time, yet, they still bring them in.

I’ve done Zillow, filtered it based on Bathroom/bedroom size, home type, etc.I’ve found a few but in the event where houses for rent don’t show up (due to time of posting ?)

(a) From the time of the sale until a redemption, the purchaser is entitled to receive from the person in possession the rents and profits from the property or the value of the use and occupation of the property.

Something that makes my situation a bit more difficult is that I have a job in Hawaii (6 hour time difference from EST. right now).

Lived there and rented half out to a roommate until 2023.

Check your local rules, but where I have rentals, the tenants need to be out by 1 pm on the last day of the month and you can organize with the new tenant what time they are moving in (eg 11 am).