Mike,
I can attest to some of what you posted, and wanted to share my experiences. I have played an E1 and two different E3's before ultimately having my own custom E3 built with Sterling Silver bell, Sterling Silver lead pipe, and brushed lacquer finish. Pitch from the E1 to the E3 is VERY different in my experiences, and much better overall for me on the E3. I've also found that certain mouthpieces don't play as well in regard to pitch. For example, a Schilke 51D will force me to push the slide all the way in, and even then, hope that my horn isn't cold! I've found that even with larger throat mouthpieces, I still have my main slide only out maybe a half inch or so, and I'm fine with that. My German Besson Prestige was the same way.
As for the valves, the tolerances are VERY tight. I recommend actually using Blue Juice for a few days to flush some stuff out (and because it's super thin), and then switching to Hetman #1. I've gone through MULTIPLE oils on this horn, and since switching to Hetman #1, I haven't looked back. Miel is actually shipping all Adams euphoniums now with Hetman #1, FYI, as they have had the same experience with this. Give that a try and let me know how that goes.
As for 4th valve pitch, I don't have this issue on C, but I have had to learn to blow a bit higher than I'm used to on low B natural and F bottom of bass clef staff, and I'm actually okay with this. I relate it a bit to playing trombone using the trigger. Again, it's something that's different, but once I've gotten used to it, I actually prefer it. I find it the same with the compensating low register as well, and my center/pitch has actually improved in this area.
As for 2/3 combination, I have had similar experiences. I tend to have the 3rd valve slide out quite a bit now and just blow up a bit on higher Gb/F#. Db in the staff tends to be very sharp (as on most euphoniums in my experience), and it is again a "lesser of evils" with this.
The triggers are now being built and shipped with the ball joint popper. A good repair tech can install the parts. Email Miel and he should just send you the parts needed. Let me know if you need any help with this.
I second you on the sound! Playing principal euphonium in Brass of the Potomac, I've noticed a MASSIVE difference in many areas. I agree with blending being easier, as well as being able to soar over the ensemble. Maybe Barry Bocaner can help speak to this as he is also a new E3 owner, and is in the section with me in BOTP!
I'm glad you enjoy the horn. Let me know how using Blue Juice for a few days (wiping and oiling each time, a couple of times a day), and then try Hetman #1. My valves are WAY faster now than when I got the horn back in June of last year because of doing this. Feel free to shoot me an email if I can help any other way.