They do in the over-the-range style, model # LMVH1711ST. It is a regular microwave with the convection mode for baking and has an easy-clean interior too. -Al

https://www.lg.com/us/cooking-appliances/lg-LMVH1711ST-over-the-range-microwave

There are a few things to check first. Like changing the HDMI cable and making sure the energy saver mode is off, but the panel has likely gone bad. I would say 90% of the time when half of the screen is out. It is either the board or the screen on its way out. It is not worth fixing these today due to the low cost to buy a new one. Repairs can be more than a new one due to the labor expense. Now is an excellent time to score a good deal with the holidays, so maybe hunt for a new one. -Al

So an actual hood vent will always perform better than an OTR microwave. They have more power and better capture space. I would do a hood first, and then if counter space is an issue, consider a micro. The best micro for this is the LG with the extend-a-vent as it is more powerful than traditional micro and works better. The model # is LMH2235ST.
For a hood that is low profile, powerful, and reasonably priced. Look at the XO model XOA30S. It is quiet as well.

If you are talking about a one-piece unit with a freezer, then the Sub Zero Pro 48″ is one of the largest. If you can do it as two pieces that join together, then the Sub 36″ all fridge can be paired with a 36″ all freezer to make a 72″ wide unit.