If you want to stay in Premiere I have done this type of thing using the audio track mixer. The trick is not to use the reverb on the clip itself but on an audio track.
1. Add and new audio track under your music track. (I assume this is just a stereo clip.)
2. Duplicate (copy) your music to this new track.
3. Cut off everything except the last second or so that you want to reverberate out.
4. Open the Audio Track Mixer then look in the upper left corner. You will see a tiny arrow. Click that and that will expand and show the effects you can add to a track.
5. In this Track Mixer window go to you new track you want add the reverb and click the top down arrow. You should see a list of effects you can add. Select Studio Reverb. Double click studio reverb to see the settings. Maybe choose “Great Hall” to start with then tweak from there.
6. When playing the timeline the music should have the reverb effect.
7. Now go to your timeline and expand this new reverb track.
8. In the timeline click the tiny diamond under the word Audio #. From here select Track Keyframes: Volume.
9. Use keyframes in the track to fade in the reverb effect. This should make it sustain and not cut off.
Hope that helps. It sounds a little complicated but if you are not comfortable sending things back and forth to audition this might be a solution for you.