1) Load Cavern Kit.
2) Replace the GB Instrument with the EXS24 (it'll automatically load the identical kit, just that now you have access to all the samples and parameters, you can generally spot whether an instrument is "replaceable" by Logic instruments from the instrument icon on your arranges track list).
3) Drag down the EXS24 "D" (decay) parameter of the amp envelope (the one on the bottom right) to your likings.
4) Save as a channelstrip/EXS preset in case you want to use it more often.
5) If you really want to use the kit more often and have even better access to individual parts (like, say, snare, kick, etc.) and parameters, load the EXS patch that you saved in Ultrabeat and resave it as a UB kit. Maximum tweaking freedom.