While I agree that the Tamron is a nice lens, just to clarify... there is no "100-400mm G2". There has only been the one, original version of that lens, so far.

That said, yes it would be a bit lighter weight option... Lighter than the Nikkor 80-400mm and a lot lighter than the Nikkor 200-500mm!

Tamron 100-400mm f/4.5-6.3 Di VC USD weighs approx. 2.5 lb. That's a full lb. lighter than the Nikkor 80-400mm (3.5 lb.)

I like that the Tamron 100-400mm can optionally be fitted with a tripod mounting ring. That's sold separately for an additional $129 and, of course, will add a little weight, but is something I'd want on a lens that reaches 400mm.

The Sigma 100-400mm f/5-6.3 DG OS HSM weighs the same 2.5 lb. and costs the same $799 as the Tamron lens. HOWEVER, the Sigma does not have the same option of fitting a tripod ring AND the Sigma is a "dimmer" lens.

While the Sigma is only 1/3 stop dimmer f/5 at 100mm, it drops to f/5.6 very quickly, at 112mm, and further to f/6.3 at 234mm and beyond.

For comparison the Tamron starts out 1/3 stop brighter at f/4.5, drops to f/5 at 137mm, drops further to f/5.6 at 181mm and finally to f/6.3 at 281mm and beyond.

The Nikkor 80-400mm f/4.5-5.6G AF-S VR is also f/4.5 up to 134mm, but it maintains f/5 from 135mm to 249mm and is f/5.6 the rest of the way from 250mm to 400mm. (Tripod ring included.)

Canon's EF 100-400mm f/4.5-5.6L IS II USM zoom weighs approx. 3.5 lb. and is f/4.5 from 100mm to 134mm, f/5 from 135mm to 311mm, and f.5.6 at 312mm to 400mm. (Tripod ring included.)

In comparison, the Nikkor 200-500mm that the original poster already has weighs about 5 lb. and is f/5.6 through it's entire zoom range. (Tripod ring included.)

A final comparison, for their mirrorless R-series Canon has recently announced as light and affordable as possible RF 100-400mm f/5.6-8 IS USM that weighs under 1.5 lb., sells for $500 and doesn't have option for a tripod ring.

Personally I have 1.4X and 2X teleconverters, but only use them with select lenses and really don't see the OP's need for them. Unless they have some other problems, it seems to me they are pretty well set with 70-300mm and 200-500mm lenses, as well as both full frame and APS-C (DX) cameras to use them upon. The DX is effectively a "free 1.5X teleconverter", where "free" means no loss of light... as with the one stop a 1.4X "costs" and the two stops lost to a 2X. Between the various combinations of lenses and cameras, they have telephoto coverage equivalent to everything from 70mm to 750mm on full frame (FX). Might just want to get a little closer. Or wait for that upcoming Nikkor 200-600mm. Or get the Tamron 150-600mm or one of the similar Sigma lenses.

Option #1, use what you have and wait to see how Nikon prices the coming 200-600mm.

Sony was the first major brand to offer a 200-600mm with excellent image quality, superb sharpness, INTERNAL ZOOMING, great quick autofocusing, short zoom rotation, superb balance (hand hold-able),OSS and more . I absolutely love it for sports, action and wildlife and it is reasonably priced at $2000 vs the amazing Sony 600mm f4 GM which is $13K USD and out of most photo budgets. .

I am sure Nikon will do likewise and aim to match that for its loyal Nikon users. The Sony 200-600mm lens has been a smash hit and huge seller for Sony, and likewise the Nikon version should be a winner also.

Hang tight and wait for that lens and its pricing, IMHO.

Cheers and best to you. FYI, I was a Pro Nikon and Canon user for four decades, both brands.

Sony A1, Sony 200-600mm f5.6-6.3 lens. A Great White Egret bends it neck to clean its feathers on the Caribbean Island of Sint Maarten/St. Martin. 600mm, ISO 1600, f6.3 ,1/2000 sec. handheld. First the full frame , then a tight crop from the same shot.

Sony A1, Sony 200-600mm lens. A Snowy Egret takes off from its watery perch in Sint Maarten/St. Martin. 391mm, ISO 1600, f6.3, 1/4000 sec.

Wild Iguanas getting cozy together in Sint Maarten/St. Martin. Sony A1, Sony 200-600mm lens, 400mm, ISO 800, f6.3, 1/2000 sec.

At a Wild Elephant Seal Rookery along the Pacific Ocean, California. A young pup squeals as it tries not to get crushed by a 5000 pound amorous bull going after one of its cows. This time this pup survived, they dont always. Sony A7RIV, Sony 200-600mm , 600mm, ISO 400, f6.3, 1/1000 sec, handheld.

Brookings Lake, Manistee National Forest, Michigan. Kids get pulled by fast speedboat. Sony A1, Sony 200-600mm lens, 600mm, ISO 800, f8, 1/2000 sec. This is about a 30% crop. I own and use my 1.4X and 2X Sony TCs and they work well with this lens, but in this instance I wanted to save the light. Frames are frames one and two of a 30fps burst.