Great responses everybody, lots of stuff I hadn't considered. Thanks!
My friend and I discussed getting simple cycle computers, which would let me know how fast I'm going. I'm not an adrenaline junkie like he is, so I find it hard to believe that I was approaching 30 MPH, but maybe...
I know of the knees-on-frame wobble reduction method, and definitely was using it. I suppose it may have helped! So did reducing my speed. I'm always trying to stay loose and relaxed, but I don't have a lot of experience with very fast downhills on mountain highways so I definitely white-knuckled it a number of times.
Yes, the stock Miyata rear rack flexes a bit when loaded. So either replacing it, not loading it so much, or both would help with that.
I will be getting my wheels looked over, definitely. I'll see what they have to say about checking the spoke tension. Going by pitch, they're all reasonably close to one another front and and back. This may just be a reality of the flexibility of the fork. My Kool-stops are quite close to the rim because the offset mounting post design means that the trailing end of the pads land between the fork and the rim. In fact, I just held the front wheel between my knees and twisted the handlebars, and was able to twist either the fork or the wheel enough to notice the gap between the pads and the rim changing. Normal?
At the moment, REI (an outdoor gear co-op of which I am a member) has an unfortunately limited selection of front racks. However, the Salsa Low Rider looks decent. Any opinion or experience with these? I think I might be able to bite the bullet and get Ortlieb Sport Rollers for the front, but the compatibility between the two is somewhat debated. There's an older video that shows how the lower attachment point doesn't seem to fit anywhere, blah blah blah, but then I've seen pictures and read reports of people using the two together. I think the compromise might be that you have to re-tighten/loosen the bottom mounting hook in order to secure and remove the panniers from the rack. In practice, this might not be such an issue, as I found that I removed the panniers from my bike very rarely.
The Blackburns are also available, and I'd get a 20% discount on those. I'm not opposed to getting them, I think I just have a totally nonsensical resistance to a front rack that doesn't make use of my mid-fork eyelets.
So, on a budget, would you
1) stiffen the rear rack by replacing it or
2) lighten the rear rack by getting a front rack and panniers
And how about those tires? At least they didn't flat! We made so many jokes whenever we had to go over a patch of roadside gravel... Is your frame compatible!? Have you changed your tires!? WHAT PRESSURE ARE YOU RUNNING!?