FYI, I asked basically the same question in a thread below, so check that thread as well in case it gets some responses.

Your kitchen is almost exactly the same as mine, down to the backsplash tile. I face the same backsplash problem when removing the OTR microwave, but fortunately I still have a box of my tile laying around somewhere. Like me, your tile isn't completely uniform in color, so even if you have to buy more, it will likely match what you have. The challenge will be if you/your tile guy mixed a custom color for the grout. Matching that might be difficult.

The other challenge I'm finding is that most good quality hoods use round (eg 7 inch) vents, whereas microwaves use a 10 x 3.25 inch vent. That will limit you in your choices. Some hoods have adaptors between the sizes and shapes but not all.

Good luck, let us know what you end up with.

I think I will likely leave the backsplash alone and just have the exposed wall refinished and painted. Maybe hang a stainless steel backplash over the stove. Anyway, that part is not a deal breaking issue like poking my eye out or gashing my forehead open would be.
The bigger issue for me is choosing the right range hood that works really well exhausting air and not becoming head bump hazard in my way in the kitchen.

I think I will likely leave the backsplash alone and just have the exposed wall refinished and painted. Maybe hang a stainless steel backplash over the stove. Anyway, that part is not a deal breaking issue like poking my eye out or gashing my forehead open would be.
The bigger issue for me is choosing the right range hood that works really well exhausting air and not becoming head bump hazard in my way in the kitchen.

The Best model in the link below looks nice and is retractable, but at $814 plus tax and shipping it will be more than I want to spend on a vent hood.

Here is a link that might be useful: RANGE HOOD

I wanted to get as high of CFM as possible, but I read that you are restricted based on duct size.
I just removed the cover plate that was hiding the ducting in the cabinet. Can you tell about how large the ducting is based on the video below?
I need to keep the existing ducting so that a simple swap of the OTR microwave for a under cabinet range hood doesn't turn into a big remodeling project.

Here is a link that might be useful: Duct video

Why don't you just cut a different size hole in the bottom of the cabinet?

"Why don't you just cut a different size hole in the bottom of the cabinet?" -- Or eliminate most or all of that cabinet above the OTR now, so you can mount the Hood at a level where it is not likely to affect your "IQ" (LOL)
From the picture, cant really tell how far above the present stove the OTR is, but most the new cooktops require the area above the cooktop to be at least 36 inches above it unless it is made of a "Non Conbustible Material" in which case the minimum distance is 24 Inches,
so If you are "Doing things to Code" this would be something to consider (If it is indeed less than those measurements now).
So You get "2 birds with one stone, wont hit head on hood and no code hassles.
Even higher, a good vent is gonna do better that what is presently there!!!

Gary

Looking at it again, I don't think hitting my head will be an issue because the controls for the stove are in front of the burners. That means the stove extends several inches out further than a 22 inch deep range hood would and would be difficult for anyone to bump into no matter what height.

The burners are a bit cramped if I use large pots, so if I ever replaced that range with one with controls on the vertical surface of the range and then more burner area that extended out the edge, a 22 inch deep range hood might become inadequate.

Here are more photos showing how far the stove extends from the cabinets

So, if I get a 22 inch deep range hood, there will be no problem bumping my head because it won't extend that far, but I will be limited with the type of replacement range I can get in the future.

I looked at the video again and noticed that there is no bottom on the cabinet where the vent is. So you could put anything there you want.

The distance from the stove to the hood is usually specified by the hood manufacturer. Some of the Kobe's I was looking at stated 27"-30" 'preferred distance'.

I don't understand how it is possible to change the height of any range hood that gets installed to replace the microwave. If it is not mounted as high as it goes, then there is going to be a visible gap of space at the top between it and the cabinet above.

You move the cabinet. Or insert a piece of trim between the vent and the cabinet bottom.