You also need the special dash speaker mount and the special radio bracket that bolts to the right hand rear side of the radio. The radio should not 'hang' from the dash mounts only.
Don't mean to hijack, but I think this is related...
I just reinstalled my radio back into the 68 and didn't notice how it mounted to the speaker bracket. It's just attached by the shafts. I'll have to look.
However, there is an about 4" long, flat bracket coming off the passenger side of the radio and angles up. I believe it has a "U" type nut on the end. Do you know where this might attach? Is this the speaker mount you are referring to? Larry