Reviews of the Barge Contact Cement indicate that Barge apparently changed their formula (ingredients) about 3 or 4 years ago and now the new formula is not very effective or durable.
Personally, I would be a bit reluctant to use any real strong adhesive to attach something that can dry and crack such as a rubber cheek pad. Although yours has lasted a long time, I've seen cheek pads that were worn out and deteriorated after only 2 or 3 years of use.
If it were me and I valued my shotgun, I would be content to just buy a new cheek pad every few years and replace the old one. At least I know the old ones can be removed without damage to the finish of the gunstock.