Moving air through a pipe doesn't really car if if it (the Pipe) is going up, down or sideways. Sure up is always better because you gain the natural rising of heated air, but plenty of setups flow down. Where do you think the air in ALL downdraft hoods and JennAir's flows??? Re: remote vs. internal- either type will work AS LONG AS the selected unit pushes/pulls enough air (cfm's) to overcome the static pressure of your pipe and all the bends. Remote or inline ones are generally quieter than hood mounted ones.

I want to echo Weed's caution about being sure on code compliance when having your vent going out near that window. Last year, when I was doing a re-routed of the vent on my range hood, the local building inspector happened by. (We are on pretty good terms so there was no compliance issue.) I asked him about the rules and got a long dissertation as he handed vent tubing up to me. The gist of it was that the rules for range hood vents are different than for those that directly vent gas appliances (say a water heater power vent). There is some discretion when it comes to venting from a range hood over a gas stove. How far the vent has to be from an opening window also varies with whether the vent is above the opening window, at window level or below window level. I was told the vent that is above an opening window can be closer than one at or below window level. BUT, you want to be sure that, if you open the window while the hood is running, it won't be sucking in the vaporous stuff that was just blown out the vent.

you always need back draft damper. what provision for make up air are you installing with 1200 cfm hood? removing 1200 cfm ( you do know that that is equal to 3 tons of hvac???) will put this area under a negative pressure. as 1200 cfm is removed, the make up air will come from any area that is not sealed. recessed lights, leaks around windows..under sole plate. you running a soup kitchen? commercial kitchen? your vent hood is way way oversized. best of luck.

“Fifty people are about to chime in and tell me you need more, but unless they have references from a non-commercial source it is possible that both they and their source have an intrinsic bias.” I only have the non-commercial reference and bias of actually having had a 300cfm hood with a 6” duct. So I lived with that kitchen with that hood for about 6 years. I can assure you it was inadequate for anything smokier than frying eggs. It was also really loud. I seared steak in a cast iron pan all the time anyway. I just lived with it, shrug; people make compromises all the time in their homes. Hey, I wanted a bigger master bath too, yet lived with the small one just fine. However, given the opportunity, when walls were open, I chose an 8” duct and more powerful hood than the measly 300 cfms I’d been living with. What a difference! Worth every penny and more. Having said that, I think 1200 cfms the OP mentioned is overkill and definitely requires makeup air. 600-800 should be good. But that may also require makeup air depending on your home. Mine is older and leaks air like nobody’s business.