Aluminum rivets. You definitely don't want to work with dissimilar metals.
In operation the forces on the boom will pull it forward, into the gooseneck. That argues for not needing to be too particular about the rivet type.
I can't think of a reason why you wouldn't be able to drill deeper holes (unless anything protruding on the inside would be in the way).
There are sites and stores that supply specialist fasteners. There may be a rivet type that works better in the geometry that you have. But you would need to fully clean out the old rivets to know what that is.