Just thought I'd update what I ended up doing - I slipped washers into the crossbar and then riveted using the standard size 3/16" rivets. It seems to hold very well and doesn't interfere with the trampoline at all. To get them in there I used a magnetic flat head screwdriver and (very carefully) slipped the washers in through the trampoline track. I then inserted the rivets in through the holes while holding the washers in place with the flat head.. It was a rather tedious process which would be made much easier with another set of helping hands.
I expect that it will get me through the season but I think I'll end up buying a new front crossbar at the end of this season as a permanent fix.
On a side note, Exactly how tight should the dolphin striker be? I tightened the bolts on the sides until they provided a decent bit of resistance, and as a result the dolphin striker feels very tight and has minimal movement in any direction. Is this too much?
Thanks for all the help by the way!