Greetings BP community- thanks for everyone's contributions. I've learned so much here, I've just closed my *SECOND* deal and am preparing to rent it out!

Here's my question. I have a handyman making several minor improvements and fixes to the unit. One of the items the inspector said to explore was the stove- it has a microwave above that was blowing air off the stove into the middle of the room, instead of up into the wall and out of the unit. The inspector suggested we try to make that adjustment if possible. There is a vertical shaft above the stove in the cabinets that goes up, but then hits a piece of sheetrock. It's not clear if this has ever been vented to the outside or not. Outside on the wall, there *IS* a set of louvers that I shined a light into, where I see a duct. One of the wrinkles with this complex is that its builder went bankrupt during construction 25-30 years ago, and so some of the finishing up was done haphazardly. It would not be surprising to find out that a venting system was started, but not finished. However, it's not apparent that there *IS* anything more in the walls than that piece of ductwork by the louvers. 

Here is my dilemma:

1. This unit was in use before with no problems. While ideally the stove would be vented to the outside, I was hoping to turn this unit very quickly (purchased 12/20 would like to be advertising by 12/30) and I'm concerned that with trying to get contractors in, figure out what's going on, and getting it corrected, especially in this holiday period, is going to add 2-4 weeks and I'm in a college town. I still have a shot to get a spring semester renter but if I'm not on the market until late January I might struggle to fill the unit until April/May.

2. Another theory I have pondered is that there *WAS* a connection to the louvers to vent from the stove but something about it became problematic. Critters? Who knows?

3. This is a townhouse. If I go exploring in the walls and something in my neighbor's unit is the issue, the coordination could take longer with perhaps no promise of resolution.

4. On the other hand, my inspector, who does good work, said that if I get a renter who does a lot of a certain type of cooking like stir-fry, not having the vent could become an issue over time. 

What's your take- would you try to open the wall and establish a fully working vent? If so, my gut tells me this is something like a $1500-$3000 job. Anybody done something like this?

All researched opinions, hot takes, and personal experiences welcome. Some photos of the view through the louvers, the view up the area where the microwave was removed, and a pic of the kitchen with the one place I think there could possibly be a vent put in if one is missing.