First and foremost, I really dig your analysis and I think you're onto something. I've been thinking along the same lines for quite a while and I'm glad to see I'm not the only one.
I see nothing wrong with your analysis written in the second post concerning volumes, mass and densities. You seem to be on pretty solid ground there.
(I'd just like to note that the calculations below are rounded to the third order of magnitude. And in some cases even this is not really deserved.)
But I would challenge some of your assumptions in the first post about energy usage. First, just so we're on the same page, I assume the 3000kL figure for antimatter comes from the TNG tech manual, page 68. But that's a volume, not a mass. You have to then assume the density to get a mass and from the mass calculate energy released. You do not have to assume the antideuterium storage has the same density as the deuterium storage. So, for example, at standard pressure and 20 Kelvins deuterium is a liquid and has a density of 165.6 g/L. At higher pressures and lower temperatures, its density is more. (Though solid deuterium is less dense than liquid deuterium.) So though the deuterium slush in the engineering hulls' storage tank is likely to be around 165.6 g/L, the antideuterium may be held at a higher pressure and have a higher density.
Using the warp power chart on page 55 of TNG:TM, I get a warp 6 power requirement of 1330 TW (392 cochrane x 3.4 TW per cochrane) which is a little more than your 1121TW, 6wf for 3 year estimate. I get that you calculated backwards from 3000 kL and 3 years but I don't get how. Dividing 3000 kL by 3 years gives me 33.7 CC/sec of antimatter. Multiplying by 165.6 g/L gives 5.25 g/sec. Adding the same amount of matter and converting to power at 93% gives me 878 TW. So how'd you get 1121 TW? What did I do wrong?
Using the 1330 TW as the power usage for the Ent-D at 6wf and extending it for three years, I get 135e21 joules released for 93% conversion to power. That translates to 1500 tonnes of M/AM, or 752 tonnes of antideuterium. To store that in 3000 kL, the density has to be on the order of 251 g/L. So it has to be under pressure. Indeed, I would argue that there has to be more antimatter than this because this is only enough for the warp drive, not the shields or navigation deflector. The figures may need to be doubled or tripled or more to include those.
But my biggest objection is the assumption that warp power usage scales proportionately to mass alone. Warp drive seems to be a geometric effect similar to (but probably distinct from) the Alcubierre drive. As such, I suspect the shape and size of the field has much to do with it's power requirements. And though we can't know what that scaling factor might be, maybe we can make some educated guesses for a first order approximation.
We can, for example, place an upper limit to scaling factor by size. Power requirements can not scale directly with the volume of the field. If that were the case then larger vessels would have no advantage over smaller ones: same percentage of volume taken up by fuel, same range;you could go just as far and just as fast in a shuttle as the Enterprise --assuming the coils could take that many cochranes of warp stress.
And, of course, the lower limit is no scaling factor: in this case it would take the same power to push the shuttle at warp 6 as it does all the different Enterprises.
Naturally, the answer is likely to be between these two extreames.
As for mass scaling, if its entirely a geometric effect then mass would have no effect on the power usage. And though I could make arguments in favor of this approach, I do not believe it: if there is no momentum involved in warp travel than there would be no need for navigational deflectors or any threat to warp ramming. Since both are canon, it seems likely that considerable momentum is imparted upon a ship going warp. Thus considerable power must be used to accelerate any mass to warp.
But is the mass scaling factor one-to-one? IE, twice the mass, twice the power usage for its acceleration? I don't know. On one hand it makes intuitive sense, even general relativity and quantum mechanics agrees with this requirement. But a symmetric, static warp field decreases the apparent mass of anything within the field. So I don't know that it's 1:1 or some other, more complex relationship.
None the less, any scaling factor needs to take into account geometric size differences of the warp field as well as enveloped mass, even for a first approximation. And for further accuracy, shape needs to be factored.
Lastly, I'd like to reiterate that I like your analysis. I think it's a fabulous first step. Further, I can think of no objections your second post, concerning density and size of the warp nacelles over the generations; another excellent step towards understanding what's going on.