You didn't accidentally use the 14 hinge hole in the mast link kit? In any case, sometimes you need someone to press down on the mast base to get the ball seated in the step socket before the mast begins to rise appreciably.
I would try to re-install the mast base if the torn out spot is not too wide. You might be able to place a washer between the mast and the pop rivet to add support to the torn side. I don't know what kind of sealant Hobie uses, but it seems a little more substantial than regular silicon. But in the very least I would reseal with silicon around the base before pop-riveting.
If you do have to cut off the damaged end, it shouldn't take off enough of the mast to hurt you, but I would either use a new mast base or re-drill the holes to be in different locations. Don't try to match the old mast base holes, They'll never line-up the same.
I always use a drill bit larger than 3/16, up to 5/16 when drilling a pop rivet. The trick is to just get the shoulder to come off and then use a 3/16 punch to push the old rivet in. This way, you don't enlarge the hole by a wandering drill bit.