BL is the product of voice coil wire length in the magnetic field (including fringe field). That means that all you mentioned affects to it, more or less, depends on parameter.
Now, depending on your starting point it maybe, and is, possible to change BL with recone kit. The possible difference comes from different voice coil and material. For example if you have original voice coil with copper clad aluminium wire and you change it to full copper one you will get significant boost on BL. Depending on copper wire thickness, you will have to adjust voice coil height to match the impedance.
Increased weight will be quite minimal so sensitivity shouldn't suffer as you will get more BL in exchange. You may even get it slightly higher.
Not Knowing what you are trying to do and why and with what driver it is difficult to say whether this is possible and feasible to do or not. It would be easy to simulate this in software, for example Finemotor which i use for driver designing.
