Prop It Up Y'All
A tri-fold shovel, available at most camping stores or military surplus outlets, makes a convenient prop-up stand for the Kawasaki KLR 650 (plus you have a good tool to get unstuck, dig latrines etc.). I got the shovel shown at right for $14.95 at Canadian Tire, and a fitted plastic case (not shown) for another $5 at Crown Surplus.
Note: before lifting the bike, have it in gear, otherwise it skitters around.
To lift the rear end, tilt it against the sidetand and prop it up as shown below. The picture doesn't show it that well, but the rear tire really is several inches off the ground so you can change the tire or lube the chain easily.
To lift the front end, prop it up as shown below. To get the front wheel up, tilt the bike against the sidestand by grabbing the fork leg. The back of the shovel blade goes under the skid pan bolt head on the frame tube; the handle of the shovel rests on the ground.