Put a "softee" on the stem backwards. Use the new button 3/8" down the stem to clinch in front of. Works well with my dentures and directs the smoke past the dentures.
I always smoke my pipes without my dentures in and I clench all the time. Your gums will become accustomed to clenching a pipe in time. If I wear my dentures I can't taste the blend I'm smoking. The recommendation by @jhowell of using a "Softee Bit" is a great recommendation.