Mike is right. There are many kitchen table stem tightening methods that work if "returning a tobacco access device to service" is all that matters.
When the pipe in question is a valuable one (intrinsically or for any other reason), though, the right fix is to address root cause of the looseness, not put a Band-Aid on it.
In every case, push-stem fit problems are the result of the wood changing shape or dimension over time, either from use or environmental factors. Which, in turn, can---but doesn't always---change the shape of the tenon (they are much more stable than wood).
The best fix for a loose stem is to make the joint "new again" by returning the mortise to a uniformly cylindrical shape with a chucking reamer, and then expanding and (if necessary) re-shaping the tenon to match.
The problem is the above procedures are difficult to do well. They require expensive tools (a set of expansion rods only costs about $60, but a full set of 1/4" to 1/2" fractional + letter chucking reamers is around $2K), and a LOT of practice & experience to avoid creating a more serious fit problem than the one you're trying to solve.
In short, if you just want to be able to smoke the pipe, any of the Band-Aid methods are fine EXCEPT the "heat & press the tenon on a flat surface" one. (Deliberately mushrooming/bending the tenon will, over time, ALWAYS distort the mortise. Then you'll have a much bigger problem down the road.)
If the pipe is a collectable or otherwise valuable in some way, though, and you want a permanent, proper fix, you must do the re-cutting & re-shaping thing.