I've read through this thread with interest, and unfortunately I have to say that the fundamental precept is flawed. There simply is no-such vehicle that can do all 3 things.
The best Tow-Vehicles ever sold in this country, within reason, were Falcon Wagons.
And they are a passable, if large, town-car.
Unfortunately their beach ability is sorely lacking (I know from embarrassing personal experience) and their (comparatively) modest weight limits the size of the van.
I've towed overweight loads, and its not something I would recommend over long distances, high speeds, or country roads. Last I checked, the law would allow (subject to OEM ratings) you to tow 150% with electric brakes.
And yeah, like many things, that works fine, in a straight line, on a good road. Personally I would stick to 100%, but that's just me. Plenty of old farts tow 3t vans with 2t cars, and not all of them have died.
(Oh, and towing above 100% with a ute with no weight at the back? Easier just to use a gun.)
Also, not sure what you mean by "special" in the context of a tow barge? Yes, you could buy a RAM. But there's a doctor in America who does an
op with a silicone mesh, and its probably cheaper.
Your best bet is to simply choose the most practical 4x4 wagon for your requirements (with an eye on GCM), and size your van accordingly.
(My personal favourite remains the GU, with the big TD, but they are getting on a bit and I've no idea on GCM.)
That will give you the best bang-for-buck Tow-Pig, a very good off-roader, and something you can live with around town.