If your legs are giving out before your heart/lungs, pedal a lower gear at a higher cadence. If your heart/lungs are giving out before your legs, pedal a higher gear at a lower cadence. That's sort of an expedient thing to try in the short term, like while on the ride.

But it sounds like the real thing to do is to build up your legs.

I would do the intervals mentioned above, alternating hammering and recovery.

Also I would go into the weight room and work on the muscles that jellify first, with heavy weights (meaning you can only do 8 or 10 reps). Leg extensions might be a good start. The idea is that if at 30 mph on the bike that muscle has to exert X force repeatedly, if X is 80% of the max the muscle can do, then its going to give out sooner, but if X is only 40% of the max, then the muscle can keep it up for longer. I'm sure there is a scientific explanation for this, which I'd be interested to know someday . . .

The other thing you might try, and don't laugh at this, is going to a spin class at the gym. There is a whole thread here on spinning, I think stapfam started it. Various pros and cons. For me, because the spin bike can be set to as much resistance as desired; because there are no stop signs, traffic, or road hazards to distract you or interrupt your hammering; and because there is an instructor and other people driving you to pedal harder - I can get a hell of a workout in just 45 min on the spin bike. The trick for me is that when the class is out of the saddle "running" and "bouncing" (ugh) I am usually in the saddle, with high resistance, pushing as hard as I can sustain. It is, come to think of it, sort of like circular weight training.

The last thing I can think of is, are you using the whole stroke? I assume you are using clipless pedals. Are you simply pushing down on the pedal? Or do you also pull back, pull up, push forward? When you are riding, try not pushing down - only pull up - you'll see that gives you some power. Not as much as pushing down, maybe only 20% as much. But now suppose you learn to pull up with one leg while pushing down with the other. You've just increased your power by +20%. Which is a lot! Especially on a hill. Your "pulling up" muscles will get exhausted very quickly at first, maybe in just four or five revolutions. So keep using them on rides, and in the weight room, and on the spin bike, and they will get stronger. On long rides sometimes I do four strokes concentrating on pushing down, four pull back, four pulling up, four pushing forward, etc. People also do single-leg pedaling drills for this purpose too. Then, when I am trying to ride fast and the legs are starting to hurt and can't push down hard enough, I remember (sometimes) to switch on the rest of the stroke and it feels like a turbocharger. Okay, a little turbocharger.

I'm sure there are more specific ways to train for speed depending on the particular kind of speed you are trying to produce. A 200 meter anaerobic sprint will need different training than a one hour time trial, and a ten minute burst of hammering will need different training too. I'm not knowledgeable about exactly what training is ideal for which of those - the road racers and track riders here will know.