Sounds to me like you need to check your belt deflection, that is, where the new belt sits in the secondary. It should sit flush or about an eighth above the top of the sheaves. If it is sitting down too far it is like taking off in second or third gear, which will cause a bog. It's also possible that the new belt is already ruined from being the wrong length or width and being ran that way. To check deflection, raise the back end of the sled up and then rev it up until the clutches are spinning, and then just let it coast back down to a stop. Don't use the brake, as that will mess up where the belt will come to rest. After doing this, see if the belt is sitting at the top or a little above. If it's sitting down too low, you need to remove the secondary and on the back there are three bolts (I think exciters are the same as mine, anyway). The way you adjust is by adding or removing washers on the bolts. The farther the bolts goes into the clutch, the lower your belt will ride, and vice versa. If your belt is sitting too low in the clutch, you're going to want to add washers (the same amount on each) to reduce how far the bolts go in. This will allow the sheaves to sit closer to each other and squeeze the belt up higher on the clutch. It is also possible for the ends of the bolts to wear down over time, and it's best to just buy new ones and start over.
Another possibility since it ate a belt, and now seems to be eating the brand new one: a motor mount has broke. If this happens, the motor torques the clutches out of alignment, which eats belts like mad and can cause the bogging your experiencing. With the clutches out of alignment, the side tension from mis-aligned clutches causes the belt to hold them out of alignment even when slowing down, and then when you hit it again it hasn't down shifted so its like trying to accelerate in too high of a gear. These two places are where I would start, anyway. Good luck.