(Disclaimer: what I'm about to say meets none of your requirements.)

An explanation that I "like" for why all artificial sweeteners can be lumped in together is that the salient effect is the taste, not some unknown biochemical effect on gut bacteria or whatever.

Penn Jillette of Penn & Teller fame had an interview where he vividly described the experience of going on a potato diet. The concept is that you eat nothing but potatoes (and multivitamins) for a month, and this "resets" your relationship with food and also resets your tastebuds in some sense. There are two effects here, so lets unpack them a bit.

In terms of relationship with food, eating bland food makes you enjoy the process of eating less, which reduces the addictiveness. Fewer dopamine hits makes the whole process less enticing, so you don't snack as much (or whatever). I'm not sure about this one, so let's just ignore it for now.

What I definitely can believe is that if you eat a lot of any strong taste, you'll get accustomed to it. Your body will seek homeostasis, downregulating the associated receptors. That's why chilli heads can eat a ton of super spicy foods, their taste receptors (or associated neurons) change over time to compensate for the level of capsaicin. My partner loves spicy food so I got used to it, but if I go travelling for work for a month and eat bland food, my tastebuds reset and her cooking becomes inedible... for a week or two and then I can eat it again. Similarly, I can drink tonic water neat, and beer tastes sweet to me. For most people those are intolerably bitter. This is not some inherent trait that I have, my tolerance of bitter flavours is because I drink tonic water regularly. When I stop for a while, I can't drink it undiluted either... for a week or two.

Sweet is no different. If you overload your receptors with excessive amounts of any source of sweetness -- artificial or natural -- they'll adapt. You will taste things as less sweet, and add more sugar to compensate. You'll add more BBQ sauce, more honey, more syrup, etc...

And therein lies the source of the weight gain.

Penn describes going off the potato diet. His friend invited him to have a burger at their favourite burger place and Penn could not eat the burger because it tasted like overly sweet cake. That's what a burger is! The bun has sugar in it. The sauce has sugar in it. The meat patty is even grilled to caramelise the outside in a Maillard reaction!

When I drink diet softdrinks regularly, burgers taste meaty to me. When I stop, I can't have burgers from most places because they taste sickly sweet. I've literally put down half-eaten burgers because they were just "too much".

This could even be tested scientifically, and it wouldn't even be a difficult experiment.

Run four groups:

1) Control.

2) Taking tasteless pills with 'x' amount of artificial sweetener in it.

3) Adding 'x' amount of sugary drinks, otherwise eating and drinking whatever the subject wants.

4) Adding 'x' amount of artificially sweetened diet drinks to the diet, otherwise eating and drinking whatever the subject wants

Where 'x' is measured equivalent sweetness, not grams.

Do this for a month or two and see if group 2 has any effect distinguishable from group 1. I bet there's no or minimal difference.

Similarly, I bet both groups 3 and 4 gain weight relative to groups 1 and 2, but 3 ought to be the worst.

I also bet that you could try different artificial sweeteners, and it wouldn't make much difference as long as the equivalent sweetness amounts were used.