The sections that matter have large enough coupling caps to be pretty ballsy sounding. I designed and built an EL84 powered amplifier that SOUNDS HUGE. The small wattage isn't the issue, it is mostly that designers reduce low-end frequency response in them in order to get a little more clean headroom.
That being said. I usually bypass or eliminate the tone stack altogether to see what the amp sounds like naturally. Tone stacks can change the sound and character of the amp quite a bit. The problem is that it is not often the best place to do tone shaping. If you know what the amp sounds like without the tone stack in place, it is often easier to shape the core of the amps sound. Then when you place a tone stack back in, you can fine-tune it to work with an amp that already sounds more like you want it.
The DT uses a lot of cathode bypass to acquire gain. The first three stages all have 10uf bypass capacitors. These will allow a fair amount of low end and is probably largely where the fuzzy gain is created. The coupling caps in the first few stages are also quite small. This is to reign in the amount of low-end reproduction from the bypass caps. Going with a larger coupling cap will increase low-end output, but can quickly get you into flub territory. You may have to do a combination of reducing cathode bypass capacitance and increasing of coupling cap size to find a balance. C1, C2, C7, and C6 are a good place to start. The most important one is going to come from V1A and its coupling cap. Reducing the cathode bypass cap here will reduce the low end and the overall gain from that stage. The coupling cap C2 is pretty small at .001uf. and really neuters the low end, but the large cathode bypass cap makes up for some of that reduction and allows all the gain that stage has to make to drive the V1B stage. So you can use these two caps in order to get the desired drive into the next stage. If you have more than enough gain, reducing the bypass cap will reign it in a little without sacrificing too much low end, especially if you increase the coupling cap size. Try the coupling cap first and go from there.
V1B and V2A are where the majority of distortion is created. The fuzzy distortion is created by the large cathode bypass cap on V1B and V2A. Reducing the bypass caps here will reduce the low end and the fuzziness of the distortion. You may need to increase the coupling caps to make up for that lost low end.
Some things to note though. Only change one thing at a time. If you shotgun all the changes at once, you will not know which one made the difference you like or dislike. I prefer to start at the front end of the amp ( the input ) and work back. This is so that I can hear how the most important stage affects the rest of the amp. This is where all the good gain is made. The subsequent stages progressively make that sound worse and worse ( distortion, phase, harmonics et all piling up and smearing things ). So you want your first gain stage to be what sets the premise.
As to sizing the coupling caps. I usually move one step at a time. So if you started with a .001, I would then go to a .002 then a .0047, and then a .01, etc. until you get what you want. I find often that by the time you go two steps bigger, it is a good time to consider moving to the next stage. a jump from .001 to .0047 is pretty big and if you don't get what you want by then, it is likely something else later that is holding things up. You will have to round-robin it a bit.
As for cathode bypass caps, it is a little easier. Once you go bigger than about 10uf, you have full frequency gain. The two extremes you could say are .68uf up to around 22uf. I prefer to go half values in the cathode bypass position until I hone in the low-end response to gain ratio I want. If 10uf has too much low end, and 5uf is too little low end, I will try and find something in between for example. As you go lower in value, the amount of overall gain will reduce as well. This is mostly in part because there is less frequency response driving the next stage assuming you don't change anything else. You don't really notice a change in this position unless you double or halve the capacitor size. The difference between .68uf and 1uf is not huge, but you can hear it. Going from 1uf to 1.5uf will not be noticeable at all, but going to 2uf will. You will have to go to 4 or 5uf to hear any noticeable difference from there. So if 10uf is too wooly and fuzzy, a 5uf cap may do the trick? You may need to increase the coupling cap of that stage to get back some low end, but don't veer too far.
Once you start changing everything by double or half values, you start straying away from the amps core sound A LOT. In your case, I would start by increasing V1A's coupling cap from the .001 value it currently has to a .002 or .0047. Listening after each change. This should get you some more balls. Then I would look to change V1B's coupling cap from its current value of .002uf to .0047uf or perhaps .01uf. I doubt you will want to go higher than one step up in each stage. Now if you get the low end that you want and it gets too wooly or fuzzy, then reduce the cathode bypass caps for these stages one at a time. Starting with V1A, reduce it from 10uf down to something lower. You can even just remove it altogether to see how it affects the sound. If you remove it, the amp should reduce in gain A LOT and you will find it thins out quite a bit too.
As an example, in my amplifier design, I have the first stage fully bypassed with a 25uf cathode bypass cap. This gives the stage a lot of full frequency gain. I am using a .001 coupling cap to the next stage and it is still pretty big and full sounding. My subsequent stages have .022uf caps though, so they don't lose too much low end as they go along.