How long does your bike sit idle when you travel?

Have you added anything that is energized when you turn the key off?  Like a USB charge port, clock or some other powered device?

Trying to eliminate the battery is likely impossible on this bike.  I am not sure how you intend to get the bike started without a battery...the electric starter on the bike runs off a battery, and there is no kick starter.  Also the decompression controller and ignition system all need power to get things rolling.  The ignition system is very sensitive to voltage and doesn't tolerate much of a drop below 12V....or it fails to make a spark.

If you can eliminate any sort of power draw when the key is turned off, a Lithium battery will last a very long time without being charged.  My bike sits for 5 months every winter - and the Lithium battery fires the bike up just fine every spring....and has done so each spring for the last 13 years.  I have eliminated the decompression controller and decompression solenoid and I have installed a manual one.  I suspect the battery will need to be replaced next year...as it does not spin the engine over as fast as it used to.

NOTE:  Most bikes that can start and run without a battery have a magneto specifically set up to provide the spark energy - and this magneto circuit is set up independently of the coil for charging a battery or providing lights.  The Savage is not set up this way and it would not be easy to modify the system to work that way.

You can add 2 two teeth to the front pully by modifying the Kawasaki EN500
https://www.motorcyclespecs.co.za/model/kawasaki/kawasaki_en500_87.htm
https://www.motorcyclespecs.co.za/model/kawasaki/kawasaki_en500_94.htm