This guy is a legend, long time home theater expert :
http/www.heronfidelity.com/blog/deal-alert.html
Frequent updates, he gets to work with the big companies directly, and very useful advice rather than always focusing on specs when asked.
As far as 1080 120 Hz is concerned, I'm assuming now that this is purely for blu-rays, yes?
My personal recommendation that fits your requirements:
https/www.amazon.com/dp/B00U313XZA/ref=twister_B00WCIJNQ0?_encoding=UTF8&psc=1
If that's not available, then you get 2 less HDMI ports, and a slightly worse build quality going with the J6200, but absolutely no big deal.
If you need more HDMI ports, then buy a HDMI switch for how many ports you like, equally as effective, although is a physical (small) box.
https/www.amazon.com/s/ref=nb_sb_noss_2?url=search-alias%3Delectronics&field-keywords=HDMI+switch
If I were you and had the room for a projector, I would go for that instead. You can get a standard throw and short throw projector for less than a TV of the same price, with hands down a better experience with a massive image.
I personally went with a projector than a new TV. I'm getting almost 80" from ~8 feet away with a Optoma HD141X. Even right now before I'm building the theater, it's in my room and no carpet, grey semi matte wallpapers, white ceiling, still better contrast, perfect uniformity, viewing angles than my LG IPS TV.
If I hang velvet and control the light more, I'm going to get closer to the contrast of VA, or higher considering even cheap projectors have insane contrast in the right environments.
All the best!