This is one of those questions that only you can answer.
From strictly a rental property analysis standpoint, $2600/mi in potential gross income for $375k is roughly a 4% cap rate - That's not incredibly exciting, but also not terrible (it's also very market-specific...it would be great in some areas, terrible in others, and I know nothing about the Metairie LA market).
That being said, we aren't talking about a strict rental property analysis, we're talking about opportunity cost:
1. If you take this deal, are you passing up on other, better opportunities? It would appear not, since you have found nothing else in the past 7 months.
2. If you take this deal, you it's an opportunity to save $500/mo compared to your current situation - What does that extra $500/mo do for you in terms of your long term investing goals?
3. If you don't take this deal, what's the opportunity cost of maintaining the status quo and paying $1300 towards your landlord's mortgage every month?
These are just some things to think about. There is obviously a ton of uncertainly baked into the economy and the real estate market right now, making it risky to pay top dollar for anything. But there's always a risk to doing nothing as well - and only you can decide which (and how much) risk makes sense for you, your financial situation, and your long term goals.