Re: tuning mark 6
I assume you mean E2 (E in the second octave), that the surrounding notes D2, Eb2, and F2 are OK.
1. Have a qualified teacher evaluate your playing habits.
2. Try a different mouthpiece to see if the design of yours is accentuating the problem.
3. Some players use tuning crescents in the E tone hole. (see www.musicmedic.com for a description of cork crescents or email info@martinmods for info on brass, body contour tuning crescents)
4. A bore insert (a blob of hot glue at the right spot, probably just above the E palm key tone hole will lower the E2 and not affect E1.)
5. See someone who knows how to analyze and align the resonances of the instrument. A sharp B2 and/or E3 harmonic can make the E2 (overblown E1) sharp. #3 and #4 may improve the situation but may only be only compensating for the combined effects of other problems, while adding more little problems of their own. In person is best. Email firstname.lastname@example.org to set up a free Skype session.