This one is a doctor thing. There are a great number of unusual metabolic things that could cause this.
The shivering. Often that's a symptom of a core temperature that's too high. It means that your skin circulation is shutting down, which of course is the opposite thing it should be doing if your core is hot, but that's what it does to some people. I've never had the shivers, even when I've been far gone with dehydration, but I've seen it in others, people putting on down jackets on a hot day, etc. But you showered, ate and drank, so you shouldn't have been in heat exhaustion, especially not that time at the start of a 300. So that's really weird, and I don't think that's it.
The really weak feeling could be a rapid blood sugar drop off. Your stomach felt bad, so I'd put my money on blood sugar gone to hell. That could have happened at the start of the 300, too. Were you dizzy? Had trouble making decisions? Any visual problems? Shivering is also a major sign of low blood sugar.
You could have had low blood sugar at the start of that 300 due to inauspicious eating, either not eating or eating an hour before the ride. A carby meal like you ate this last time will frequently drive down blood sugar. I never do that, because I'm relatively sensitive. I have to have small amounts, frequently. Machka mentioned that. I've eaten a meal before a pass climb and then almost fainted off the bike during. Also that happening that time before dinner could be the same cause, from improper fueling during the couple hours before it happened - either lack of fuel or a change in fuel, like going to a sugar drink from a slower fuel source, most likely.
So I'd think about my diet, and exactly what I'm eating and when. Do you eat mostly carbs normally? Frequent carb snacks? Maybe go in and get a glucose tolerance test. I'd definitely ask a doc to schedule one. And then think about everything you eat and ate that surrounds these events and the timing of that eating, and see if there's a pattern.