I am going to chime in with a little bit of (possibly incomplete) information that I am aware of (or believe to be true and pertinent)
You must cross hatch or hone your cylinders when you replace the piston rings. I was told (informally) that two fold, the newly roughened surface aids in the new rings being seated to the cylinder mating surface. [side bar] If you just replace the brake pads without resurfacing (or glaze breaking) the rotors, the pads will not seat on the rotors and you will only have partial contact, thus less braking ability] So in that sense, if you just install new rings on a glazed and polished cylinder bore, there is not any microscopic rough surface to aid in the wear and break in of the new rings. You may have been better off leaving the old rings in there as they have already been shaped and polished to the current cylinder profile.
Basically, your break in period, is a period of all the parts being worn and polished to perfect the microscopic fit of all the components to one another. If you were to monitor everything that is going on, you would note that compression increases over time of correctly breaking in period, and temperature will slowly decrease as the parts polish and friction decreases.
Remember it is called cross hatching, so while you are spinning the hone, you need to be always moving in and out of the bore. Don't just put a hone stone in there and rotate it quickly without aggressively moving in and out of the bore. Slow to moderate rotation and a balanced in/out movement all the while lubricating to remove particle matter. Think wet sanding a paint surface with fine grit sandpaper. You use the water to keep the cutting surface of the sandpaper from clogging with the dust...
Also, the cross hatching will hold more lubricating oil for the break in period, and assist in carrying the wear metals away (well, this is true in crankcase engines with oil bath and I can imagine somewhat similar in two stroke also)
Which inspires another comment for discussion, in two stroke, use additional oil in fuel for initial break in?
And we are air cooled, I know with aircraft engines, we do not run them much on the ground, (especially with the cowling removed) they need to be flown a certain way that puts the most cooling air across the cylinder fins for cooling (shallow climbs), and shallow descents (powered) descents to avoid shock cooling the cylinders.
If you overheat the cylinders during that break in period of high friction, you run the risk of galling the pistons.
So maybe, we should start a freshly honed cylinder with new rings, run it for an initial period (in tall grass like someone previously posted) but for a limited period and then let it cool off. Then an little longer run with a heavier load, but keeping in mind not to run it too long and getting too hot.
I was told one time to drive it like I stole it, and other said to baby it during break in. I know with aircraft engines during breaking, it is common practice to continually change the power settings so as to not "groove" the engine to being used to just running at one particular power setting...
I apologize for being so long in the finger. I like to learn and teach what I have learned. If I openly run my keyboard, maybe someone will point out where I am thinking wrong...