How old is the Burley? The distance between studs (meaning how far the stud is away from the rim) for mounting the brakes has changed over the years. Newer cantilever and linear pull brakes will not work with the older standard. If you use a very skinny rim, you might be able to get them to work, but not the best. The symptom is as you describe, the arms will be angled out and it is difficult to get the pads to hit the rims.

If you want to use linear pull brakes, there might be an option. The new Shimano CX-xx brakes might work. They are made for cyclocross. Shimano has moved the arms out farther than other linear pull brakes for mud clearance. To get the pads to hit the rims, they use a long spacer. These brakes come with different spacers and by using the shortest of the spacers might give you enough clearance to use them with the older standard.