The two mouthpieces you are comparing (Schilke 14A4a and Bach 2-1/2C) are examples of a fairly shallow, and very deep trumpet mouthpiece. For example the 2-1/2C actually is deeper and more bowl shaped than a Bach 1-1/2C, which is a big orchestral mouthpiece. You can compare mouthpiece cup profiles here.
http://www.kanstul.com/html/products/mouthpiece_compare.html
Since your background is in cornet playing your sound concept for trumpet probable reflects that, meaning you like a dark, full sound. That might be why you are drawn to the sound of the Bach and do not like the Schilke. Since mouthpiece design is always a bit of a trade off, any more shallow mouthpiece that makes the upper register a bit easier will generally have a characteristic sound that is thinner and brighter than a deeper cup, especially when playing in the lower register. There is nothing you can do to make the 14A4a sound much different. It sounds the way it was designed.
So there are a couple of options. As suggested above you could accept the tonal characteristics of the shallow lead piece as doing what it is designed to do, and use it for lead while using the Bach for other applications, or you could try to find a mouthpiece that is a different kind of compromise (all mouthpieces are a compromise).
You might consider any one of many mid sized diameter mouthpieces with a medium or medium deep cup. There are lots of examples. Bach 3C or 5C, GR66M, Curry 3C, Yamaha 14C4, Monette B4, B4S or B6, Warburton 4M or 4MD are all in that range. Any one of these would probably improve the ease of your upper range and produce a sound that you prefer to the 14A4a. It is not that they are better mouthpieces than your Bach 2-1/2C. It is just that they are more middle of the road in terms of cup volume.
Cheers,
Dave
www.wedgemouthpiece.com