Your T/C Hawkins was a kit gun. This is indicated by the K at the beginning of the serial number. Also the Hawkins is a 1-48 twist. That means it will shoot roundball and conicals.

Since you're hunting elk, I would go with a conical. Some of the conicals to try would be a maxiball, Great Plains Conicals (they come in a lot of different weights) in the 385 grain class, and another conical to look at would be a 348 or a 405 powerbelt. Maybe the Platinum type. Other bullets to look at would be some of the Bull Shop conicals in a 460 grain or 495 grain.

Also you don't have to push big conicals as hard as you might thing. 70-90 grains of powder produces some impressive down range energy. If you can work up a good accurate conical with that kind of powder you should be in business out to 100 yards.

Another thing you might want to keep in mind is wads. If the conical has a flat base, like the maxiball and the bull shop.. often times a felt wad can help with accuracy...