Does it even have central air in it, and would a buyer expect it there?

There is a ton of experience on this site and I would love to hear how to avoid mistakes or prevent something I can't handle right now.

I'm guessing in order to prevent further flooding I would have to dig out the concrete floors and re-locate the sub pump more to the middle.

House flipping attracts countless business people like you, but not all of them make a profit.They make preventable mistakes.

I am considering replacing a split system air conditioner/furnace in a 1000 sq. ft. 3/1 rental home with a new 2 ton AC unit and a 70k BTU gas furnace.

FYI- It is not the responsibility of the landlord to make sure the tenant pays the electric/gas bill  Ironically, Air Conditioning is not required. 

The mechanicals were boiler fed baseboard heat and hot water, and no air conditioning. 

Good thing that it’s only $700/month loss in income, but I think it prevents me from going with strategy 1 or 2, because then I’ll have to eat about $600/month until I can fill these vacancies.

The thing is, there will come a day when the Air Force will tell me they don't need me any more but I'll still have my family to think about.

May be able to do some preventative maintenance that will save you a headache down the road.