Oh boy I fought one of these for over a year, same thing
tried everything!!
Reluctant to say, it was a simple fix. Fuel line routing. The factory fuel line runs kinda close to the exhaust and it boils the fuel. Rerouted it, fixed the problem.
Another potential issue (and probably don't have much to do with it dying after 15min), the original fuel pump has a "weep" hole at the bottom of it. If the diaphragm in the pump dies, it will leak fuel onto the muffler, and it usually make big fire. If you have this style pump, replace it asap. The new pump has a nipple on it which is where a hose goes, you put the included hose on it and route it away from the muffler. MUCH less fire potential. Fire no good (as stated by a japanese engineer at kawaski).
normally spark related stuff, won't run for more than 5 minutes. NORMALLY. That and kawasaki spark related issues are kinda rare at least on that kawasaki engine. Some of the really old stuff different story.
easy way to diagnose. Go use the mower normally. When it begins to die, choke it immediately. Does it pick up and run a little longer? If yes, you have a fuel problem. If no, you likely have a spark problem.
on the igniter box ohm test, the test is inconclusive and I don't even rely on it. I had (might still have?) a known good one I use to test. Plug it in, if it runs better, that's the problem.