When the RAF introduced the 3 inch rockets (in Tunisia IIRC) they were originally fitted with the AP warheads in the anti-tank role. However, when a Hurricane squadron was sent out to stop a group of Tiger tanks they found the new weapons just bounced off the armour. Later on, someone had the idea of trying the HE heads instead and these were much more successful. Although the HE couldn't penetrate the panzers' armour, they were able to blow off wheels and tracks, or even turrets on some occasions. Also, there was a useful anti-personnel bonus in using the HE heads.
The 16 rocket load was actually 8 doubled up rockets. Two rockets were strapped together and hung off a single rail and then fired as one.
Ironically, the RAF's anti-shipping aircraft switched from the HE to AP heads. They found that by aiming them a little short of their target, the rockets would turn horizontal on hitting the water and then penetrate the ship or sub's hull beneath the waterline.
These heads just screwed on the standard rocket bodies, so there is no reason the Tiffie couldn't have carried them. I've never heard of them having done so though.