jek, all rivets have a work range or min/max thickness they will handle. sounds like you just need shorter rivets. another way of dealing with too long a rivet if its not too long is to find some small washers that just fit over the rivet body, use metric washers if you have to. sometimes there thicker then standard washers anyways. you put the rivet through the hole and you put the washer over the rivet before you crimp it obviously.
if the rivet is way to long this obviously wont help but if it just a tad too long this trick works great to get a good tight crimp on the rivet. I use thick small washers on everything I pop rivet. the washers give a biger surface area load then just the diameter of the rivet itself. sheet metal is in a soft condition or just not heat treated, so it can crack or the rivet can pull through easier then if it has a hardened washer backing it up.
use grade 8 or washers that are heat treated. a crack can develop at a rivet, the washer will help eliminate that problem. if I remember correctly we used washers on all the aircraft seats we would build for added strength of the riveted joint and to minimize the posibilty of cracking. you can even use a washer under the head if you need to and if its not a problem with how it looks. use SS so they wont rust. sorry I forgot to tell you about this before. I have forgot so much of the info about riveting tricks I used to know since I dont do it anymore as a job, but thats ok, this kind of thread does jog my memory.