Thanks for the comments everybody. Believe me, it's even worse watching it back knowing it's my own footage. The second clip and its overlaid text is a little misleading because I don't have the footage from before that clip starts. It makes it look a little worse than it actually was, but only a little.
What scaflight mentioned with mapping the stick is exactly what I had done when I first started flying it and offline it worked well enough. However, that doesn't cut it when you're playing online vs. F-15s and Su-27s and every second counts.
I spent a few minutes this morning with a completely new set of control bindings and I now feel a lot more comfortable. Things like having the IFF and jamming filter bound are incredibly important when playing online. You don’t have the time to waste clicking things in the cockpit. I've also moved all the radar commands such as high angle, beam, and radar on/off to much faster to reach places.
I ran through the hardest version of the target practice mission several times after that and I even though I'm not fully used to these new bindings I can immediately tell that I'm already much quicker and make much less mistakes.
A lot of it comes down to experience and practice, and that first night online was a rude awakening to how good I thought I was operating the weapons under pressure. Still, I am pretty proud of myself for having maneuvered myself into kill shots on three occasions. That I fumbled with the controls is unfortunate, but that's the easily correctable part if you ask me.
Oh, and about the canopy frame, I never realized how restrictive it was until those online fights. Your forward view is really limited, and you have no rear visibility at all. I had a hard time keeping track of targets because they would get lost in the armored canopy. It can be helped by putting your head up to the glass, but it's something I need to be very wary of.
Despite getting shot down more than a few times (and flying into a mountain or two) I had a boat load of fun. I'm out of town for the rest of the week, but I can't wait to give it another go when I get back.