Hmmmm. That聮s an interesting one. Have you tried any of the newer LED-based hiking headlamps? 聮s Corona LED Headlamp ($55), for instance, puts out an impressive 65 lumens on all eight of its bulbs, and can be dialed down for more battery life. It takes three AAA batteries that fit into a case that sits at the back of your head, and will give you 30 hours of light on the high setting. You should be able to run pretty well with that.

听
聮s Myo ($89) puts out even more light聴150 lumens (equal, roughly, to an eight-watt incandescent bulb, which isn聮t bad!). And even more battery life from three AAAs聴80 hours on high. Very impressive.
Your next step is to enter the world of cycling lights. Which might not be a bad idea. 聮s Minewt 200 ($199) throws out 200 lumens, enough to bike with, so certainly enough to run with. Niterider makes a headband mount ($20) that supports it nicely, too. You聮d have to deal with the battery, but it fits nicely into a pocket or a very small fanny pack, offering up to three hours 30 minutes on a single charge. And it IS rechargeable. So that聮s a good thing.
听