Beekeeper, I hear ya. We all have our personal worries. My approach is a little different. I try to face my fears and learn to handle my motorcycle in the scenario that concerns me. For that, I regularly go to the track (instructor). For the issue you just described, I would urge you to find an instructor / school which offers a dirt course.
Yeah, like anyone can really 'learn' how to handle a catastrophic motorcycle tire failure. Despite macho "I can handle anything due to superior experience and training" attitudes, we MAY be able to get the bike under control and stop safely, but, depending on the nature of the failure, we may not, no matter how good we are.
No amount of training can overcome physics. Gravity makes stuff fall down - and a flat tire on an inherently unstable two-wheeled vehicle can take down any rider, no matter how experienced or well-trained. Yes, some experience in unstable surface riding may help when the time comes, but off-road riding experience won't do much for a blow-out on a heavy paved-road machine like the GTL, and I have experience in both scenarios.
In this year's Iron Butt Rally, a rear tire failure took down a very experienced rider, on a flat, straight section of highway only 5 miles from the finish - this was an IBR multiple-rally rider with many years of other rally and riding experience - one minute contempating the finish of an 11,000-mile 11-day epic, the next minute tumbling through LA rush-hour traffic, with the BMW GSA totaled.
Compared to any other vehicle, tire failures on motorcycles result in a much higher percentage of resulting accidents. It is the nature of the beast, and therefore incumbent on riders who care about their skins to ensure that this element of risk is minimized - whether replacing a tire with thin tread before the wear bars emerge, or swapping out a tire that was flatenned by a nail just in case there's a hidden cord cut... I would NEVER ride more than the distance needed to replace any tire that has gone flat for any reason. It is also smart to replace any motorcycle tires that are 6 years old, regardless of wear, and any car tires over 10 years old.