Once the mortise is sized, squeeze in equal parts of your favorite epoxy. I mixed them right inside the bottom of the mortise.
Insert the portafilter shaft into the handle and watch for squeeze-out. Wipe off any excess epoxy with a paper towel. If any epoxy gets on the wood, it's no biggie - the epoxy can be sanded off once it dries.
Let the epoxy set for the recommended amount of time and then some - I noticed that the large thermal mass of the portafilter significantly increased drying times by keeping temperatures low, and therefore slowing down the chemical reaction which dries the epoxy.