So I did a quick comparison of the schematic for the Studio Preamp (not the Studio Caliber Preamp) versus the only schematic that I could find for the Mark III (there are lots of variants within the Mark III line, so who knows what's in yours). In reading your post, I saw comments like "[how] sparkling the clean tone is" and "[Mark III's] midrange presence peak", and "[Studio's lead channel's] smoothness and fluidity". And, while it is true that all the Mark amps (except the Mark I) share a common circuit architecture, they all have little tiny variations that do affect the tone. So, here's what I found...
I'm going to start with the "smoothness and fluidity" comment. For the lead channel...especially for single note lead work and not power chord chunka-chunka...the smoothness and fluidity is often a function of having some bass in your signal when it hits the tubes providing the distortion. Usually, bass is a bad thing this early in the circuit because it makes the distortion sound "flubby". But, to get a good liquid singing lead tone, you need to have some bass. If you detect a difference in smoothness, it could be that the circuit elements that manage the bass are different.
When I looked at the two schematics that I had, I found that the very first tube stage has a cathode bypass cap of 15uF in the Studio and only 0.47uF in the Mark III. The larger the cap, the more (and deeper) bass is included in the mix. The difference between 0.47uF and 15uF is a really big. Your Mark III, however, should have a "Pull Shift" on the bass knob. If you pull the knob, it brings in another cap to increase value to just about the same as you have in the Studio. This is a good experiment. Fire up the Mark III, put it in lead mode, pull the bass knob, dial it to a similar value as on the Studio, and noodle away. Does it have more "smoothness and fluidity"?
The presence of bass early in the circuit also, in my opinion, reduces the apparent "aggressiveness" of the distortion sound. So, when you do the "pull shift", do you lose some of the aggressive character that you like in the Mark III?
There are other spots where the bass is different, too...such as the decoupling cap after the tube that just precedes the EQ. The bigger cap (Mark III) let's through a little more bass and the bigger cap (Studio) lets through a little less. But, this is pretty late in the circuit (post distortion), so I don't think that it would affect "smoothness", "fluidity", or "aggressiveness". But, a comment made in the new Mark V manual makes me think that it may have some effect on how you feel about the Studio vs the Mark III...
In the manual, the Boogie guy talks about his favorite Mark IIC+ and how he feels that the non-EQ versions of the Mark IIC+ sound better to him. When they tracked down the difference, he said it was because of a particular cap that is smaller in the non-EQ models and larger in the EQ models. Well, in my interpretation of his words, it looks like he's talking about this one decoupling cap. And, in your Studio, you've got the smaller version and in the Mark III, you've got the larger version. So, maybe you're feeling the same difference that he felt.
Now, as for the differences in the clean sounds, this is a little more difficulty. The warmth, clarity, chimy-ness, sparkling, etc, can all be strongly influenced by the voltage level produced by the internal power supply in the amp. In my opinion, a higher voltage value adds clarity and precision at the cost of warmth and character. Sadly, I don't have the voltage numbers for the Studio, so I can't compare the two amps. The "Sparkling" adjective, though, is different to each person. I feel that it is usually most affected by the particular tubes that you have. Try swapping the pre-amp tubes between the two amps and see if the mark III gets more "sparkling".
As for the "presence peak", that can also be affected by the pre-amp tubes. Swapping the tubes might change that. Another option is that the frequency shaping elements are different. We already spoke about some of the bass management elements. These probably don't affect the "presence". "Presence" makes me think treble. The Mark III has a slightly different slope resistor in the tone stack, which acts to add a smidgen more bass and doesn't affect the treble, so that's not it. The Mark III has a bigger "Treble Shift" cap, which would make it a bit more mid-rangey when engaged, but I assume that you do not use the "Treble Shift" when you're playing clean. If you do use "Treble Shift" when clean, that could be your difference. Otherwise, I'm not sure what would cause the difference in the presence peak. Voltage or Tubes are my best call.
Sorry for the long post. Give my suggestions a try. Good luck!
Chip