From what I've been able to find out, the 'normal' guitar shape does indeed affect the tone. It gets pretty complicated, as does everything having to do with the guitar. Basically, when you have a figure-8 shape with a reasonably pronounced waist that is higher than the mid point of the length, and there's a sound hole a little above the waist, AND the top, in particular, vibrates, you can get a complex resonance couple that causes at least one of the 'air' modes to 'split' into two modes at different frequencies, one of which can put out significant sound from the hole. If any of the conditions is relaxed the resulting single mode does not put out much sound: 'Dreadnought' shaped guitars, for example, don't usually show this split, and it's part of the 'characteristic' timbre of the breed.
What it comes down to, then, is that, while citterns and so on do sound OK, they don't sound like a guitar. If you want something that does, you have to make a guitar. There seems to be a reason why we've been making them that way for so long.
It seems to me that we can learn from the violin players in this. It's a rare violinist indeed who does not use a chin rest and shoulder support. There are lots of different shapes of chin rests, and no matter which one I put on a fiddle that I make it's the wrong one. Shoulder supports come with several adjustments for the height and angle, and again, you see all of the different settings being used. I strongly suspect that any 'ergonomic' shape you came up with would be a poor fit for some large part of the guitar community. It would be difficult to change it, and it would take some time to learn to get a 'guitar-like' sound from it.
The 'wedge' guitar body shape, shallower on the bass side and deeper on the treble, was patented back in 1969, iirc, by a fellow named Smith. Linda Manzer had not heard of it when she devised the shape for the 'Pikasso' guitar that she built for Pat Metheny. It is such a beast that she had to do something to make it possible to play it, and she came up with the wedge independently. At some point she mentioned it to another maker, who forgot the conversation. Some time later he, too, 'invented' it, and claimed priority. It took some time for Linda to clarify the situation, as she understood it, and she promoted the idea of the 'Manzer Wedge' to establish her claim, although she never asked for royalties so far as I know. A few years ago a student of mine came across the original patent. Linda and I have exchanged a copy of the patent and (cordial) e-mails. There is no doubt but that she came up with the idea independently, and deserves credit for that. The fact that it was patented indicates that it was one of those things that was 'in the air', and somebody else would have come up with it if she had not. At least it has stayed discovered since then.
I have often wondered what a cutaway does to the sound, but it's hard to think about how you would figure it out. There are 'minimal' cutaways out there, using a 'bevel' shape that only removes wood from the side and top, with very little change in the air volume or distribution of the box. This is often all the cutaway a Classical guitarist would need, if they need any at all. Steel string players who use 'thumb over' technique find it more limiting.