@Nick Diecidue you can always ask the seller to deliver the units vacant upon closing (that's if you haven't signed a P&S yet).
What I would do is buy the property, and right away have the tenants fill out a rental application, apply that information into a 3 month lease, and deliver a notice of non-renewal 45 days in advance. Basically you are saying "im giving you 3 months to find a new place". This way you can collect a few months rent, and get your ducks in a row for the renovations.
@Nick Diecidue Your budget is way, way too low. You couldn't do the work yourself (material only) without permits for the money you state. Plus, in NOLA, you will need permits to complete the plumbing and electrical work by licensed subs. There is NO way to get another meter without a licensed electrician with permits, plan and simple. Is the property zoned for a duplex, if not you will need a variance from city hall with is another headache.
Also, you do not want to make tenants live thru a large renovation as you mentioned. Adding a bathroom will be a big renovation. I would have any tenant vacate house prior to the renovations. Its doubtful they will be willing to pay the increased rent (they obviously like the size and price as is).
If you are splitting the electrical service, its very, very likely the entire electrical system will need to be brought up to current code. Personally, I would budget at least $3500 for separate service, and that assumes the existing service is all up to code.
Lastly, are you sure about the rent numbers? A $800/month duplex is not good rent and likely in a marginal area of New Orleans. If that is the case, I doubt you would get $1200/month for a 3 bedroom unit.
While I am guessing because you did not give much information at all, I would bet the renovation would be closer to $20k for what your talking about doing.
You plan to renovate while the tenants are in place? Have you thought through the logistics of this? Even small improvements never go as planned, bigger jobs will have delays and unforeseen problems. doing this with tenants in place could prove to be disastrous.
@Troy Williams All of my contractors and subs that I deal with are new construction or full gut rehab guys. If its light rehab, your likely better off finding a decent handy man, which I use (anything light I do myself). Expect decent guys to be busy, as its quite busy in the area for construction.