In the army we were taught a method called S.P.O.R.T.S.
Slap the magazine up
Pull the magazined out
Obeserve the chamber
Replace the magazine
Tap the magazine
Shoot
I think you are getting a little rusty, cause that isn't the proper sports procedure.
For the M16 the procedure we teach is:
Slap the mag
Pull the charging handle
Observe the chamber
Release charging handle
Tap forward assist
Shoot
This is the correct SPORTS procedure-- which is often called Slap-Rack-Squeeze/Tap-Rack-Shoot or various similar things but it doesn't deal with a double feed. Don't get me wrong, your malfunction drill should always begin with Slap-Rack-Squeeze/Tap-Rack-Squeeze/SPORTS but it doesn't always work.
My next procedure is to
Rip the magazine (I tuck the magazine away, either in my duty belt or in a pocket because I'm not going to reuse that mag unless I go through my other mags first. It also gives me the ability to use both hands on the weapon)
Rack the slide
Reinsert a fresh magazine
Address any threats.
I don't typically rack it three times because I don't remember being taught that except to administratively clear a weapon. LE usually don't end the shooting session with a cleared weapon sitting on the bench, we usually have weapons. I may reconsider that racking three times bit since everyone seems to be teaching it.
No matter what you do, you must be do it quickly.
I agree that moving to a secondary weapon is the best option. We practice that all the time, but not everyone carries (or is allowed to carry) a backup. The decision of whether or not to move to a backup weapon (BUG, knife, baton, spray, radio, potted plant, chair, fist, etc) or to clear the malfunction must also be made quickly.
Just as you should practice (or simulate at least if you are at a restrictive range) moving laterally while shooting, you should also be moving laterally or to the closest cover while completing the tap-rack-squeeze or unload-load drill.