It's time...
It's past time.
The downside of taping the frame package is that the tape may not allow the mat to expand or contract freely with changes in the environment. Being too tight in the frame as artfolio mentioned is one cause of cockling, but restricting the mat in any way can have the same results. If you are going to tape the package, the most dimensionally stable element, normally the glazing, should be the largest with all more active elements, mat and mount, slightly smaller. That said, you still risk cockling when environmental conditions are right.
The mat will probably need to be replaced. Once it has deformed and then set in the new shape, it is difficult to get it to revert to the original flatness. You might try the heated vacuum press as Peter mentioned, but I would be inclined to replace the matting.
Another reason to take it apart is to see what's going on inside the mat/mount package. Cockling is often an indication of a spike in humidity at some point in the past and with moisture comes other issues that should be looked into and addressed if needs be.
Ideally, works on paper should be removed from the frames and inspected on a regular basis, and 15 years is not the preferred interval. More like every 3-5 years depending on the environment.
The efficacy of taping the frame package is debatable. It does make for less work in the fitting since loose debris in the frame can't transfer to the frame package, but the presence of pressure sensitive tape, and the question of not what you seal out, but what you seal in still exist. Even sealed frame technology has been challenged for claims of long term protection.