You make some good points. Allow me to suggest one correction and add some context.

1. The new OM Systems lens is 150-600mm, not 180-600mm.
2. The focal length of 150-600mm f/5-6.3 lens on a micro 4/3 camera is equivalent to a 300-1200mm lens on a full frame camera.
3. The Nikon 180-600 mm lens without the tripod collar is four ounces lighter than the OM 150-600mm lens, but if you add a teleconverter to the Nikon lens to get a focal length greater than 600mm, it will exceed the OM lens weight by four to six ounces.
4. To achieve the 1200mm field of view on the Nikon 180-600mm f/5.6-6.3 lens, you would need to add a 2x teleconverter which would give you 360-1200mm f/11-13, and you would need to raise your ISO two stops higher than the OM system, and the 2x teleconverter would result in a softer image.
5. Regarding lens weight: Two lenses can weigh the same, but the distribution of the weight in the lens is very important. If the lens center of mass is closer to the camera, the lens will be much easier to hand-hold than if the center of mass is further away from the camera. Unfortunately, data to assess this factor is not available for either lens.
6. The Nikon lens has a minimum focus distance of 4.5 feet; the OM lens has a minimum focus distance of 1.8 feet which, with its 1200 mm reach, gives it a macro capability.
7. The OM lens has sync-IS, which means the lens IS and the camera IBIS work together to provide 7 stops of image stabilization. The Nikon lens provides 5.5 stops of image stabilization.
8. The OM lens does not have internal zoom, but it does have an IPX1 certified water sealing and a fluorine coating on the front element. I don't think the Nikon lens has a weather certification, but I expect it to perform just as well in wet weather.
9. The OM lens also accepts teleconverters, but I recommend a tripod if you intend to use it at its 2400mm limit.

Okay, some corrections on your corrections. First the reach on a cropped camera (like the OPs) is actually 1.5 times the focal length. So their 600mm is actually 900 mm. Putting a lens on a cropped sensor does not change a 600mm lens into a 1200mm lens. To me, one can always crop. The high density of pixels in the OM system means less light per pixel so the aperture equivalent also changes. And as you mention, the distribution of weight is important, and not having an internal zoom means that the centre of the weight is going to change when you zoom. Having used the Nikon 200-500mm, it is quite annoying, especially when used on a gimbal. So I strongly prefer internal zooms (like the 150-400mm).
Did you buy this lens? I haven't felt one in the hand and tried to zoom out and see how that feels. Have you?
I know that OM system can be used to get great photos. I can even imagine buying one in the future. Hopefully when they make a lens I like. This new lens is not going to convince me to switch. Reach is important for me (as well as image stabilization) but so is weight, ability to shoot in low light and cost. My current Z8 allows me to hand hold my 400mm f/4.5 lens on a rocking boat and do video, so at this point the image stabilization is sufficient.
I would love to do a comparison at some point, too bad the 100-400mm IS doesn't work with that of the OM-1 camera (love the weight of this lens) so only 3 stops of IS.
PS. Example of a video shot handheld on a rocking boat with "only" 5.5 stops of IS:
https://www.flickr.com/photos/60519499@N00/53080006403/in/album-72177720310122074/

What are you looking to confirm? You've asked about different sensor formats (crop factors), although they all overlap in the 20MP to 24MP range.

That is: the Nikon DX crop-factor is 1.5x. Your D7200 is a DX format at 24MP. Your D500 is a DX format at 20MP. The aspect ratio is 5:3.

The OM System OM-1 is a micro four thirds, with a 2x crop factor, at 20MP. The aspect ratio is 4:3. The camera is mirrorless.

Of course, all the mirrorless benefits vs DSLRosaur apply. The OM-1 is their flagship model, maybe something that would apply to Nikon's DX DSLRs in the D500 release, not something that ever applied to the ancient 2015 D7200 release.

A few OM pluses: 1. 5 axis internal stabilization, reputed to be the best in the business 2. Less obtrusive 3. Supremely water resistant, dust proof, and still works well below zero. The only time I need a tripod is if I’m doing HDR, bracketing, fireworks, astrophotography. How water resistant you may ask? I took what would now be an 8 year old Olympus on Maid of the Mist and to cave of the Winds at Niagara Falls with no protection for my camera and it functioned flawlessly! Can Nikon boast the same? And, yes, the lighter weight is a plus. As to the lens… Oh, and image quality, oh that! Far better than anything I captured with my Nikon.

I am a m43 user and not offended at all re the issue of why jump into M43. M43 is a very specific camera system. It has limitations that the user really has to know about and deal with.

Unless I needed M43 for travel, or wanted to really downsize to the OMD em5 and smaller lenses I’d just sty with Nikon.

Also that beast of a lens is pricy, heavy and really would only be used effectively by a small number of photogs. 150 to 600 is equal to 300 to 1200 in ff terms. I can’t imagine wanting or using it.

The Oly pro lenses are very special super sharp great lenses. But getting into all that would cost a lot of $$.

I don’t think the juice is worth the squeeze in this case. Stick with the gear you have.

I am a m43 user and not offended at all re the issue of why jump into M43. M43 is a very specific camera system. It has limitations that the user really has to know about and deal with.

Unless I needed M43 for travel, or wanted to really downsize to the OMD em5 and smaller lenses I’d just sty with Nikon.

Also that beast of a lens is pricy, heavy and really would only be used effectively by a small number of photogs. 150 to 600 is equal to 300 to 1200 in ff terms. I can’t imagine wanting or using it.

The Oly pro lenses are very special super sharp great lenses. But getting into all that would cost a lot of $$.

I don’t think the juice is worth the squeeze in this case. Stick with the gear you have.

Not sure why you are asking the question, if you mostly use your D500, why ask about the D7200 versus the OM1? The D7200 (and D500) is a completely different camera than the OM1, which is a micro 4/3 mirrorless. Assuming that you have only Nikon lenses, you will need to get an OM systems lens? Have you picked out which? I have heard good things about the OM-1 camera but my personal view is that I wasn't thrilled at the lens choice for wildlife photography. Micro 4/3 users always are going on about how lightweight their system is, but the "replacement" for the 100-400mm lens (the 180-600mm) is much heavier than many Nikon lenses and even heavier than their 100-400mm TC f/4.5 lens. Some day I may switch to the OM system (I have both the D7200 and D500 and happily used both for many years but mostly use a Z8 these days) but would want an updated light weight "long" lens before switching for my wildlife photography. That is purely my view as a Nikon user.
I am sure there will be many OM users who will be offended by my comments, but are you really excited about their new lens, the 180-600mm? It is $1,000 more than the Nikon 180-600mm, doesn't have internal zoom and weighs more than the Nikon lens.