That kind of electric power, that is available on most bikes, resulted in that I installed more electrical power on my Suzuki GS850GN. Then I got a beemer, since they had a rep of having a powerful alternator... the rep proved not true, so I installed a better alternator on it as well... now I have yet a beemer to fit with a stronger alternator and this time it will be a Bosch 90A (1260W) which is somewhat more power than what your KLE alternator delivers -
I.e. - you need to either enhace the alternator capacity, (Z1300 Voyager, USA issue, hade double alternators - could Kawa fix that to the KLE as well?), or swap bike to one that has.
Here is what I did:
Alternator:
http://www.webstruktur.com/svea/board/artik/bilgen.html
http://www.webstruktur.com/svea/board/artik/mont_bilgen.html