Impulse Tracker had it: the Note Fade new note action.
It lets an active note ring out in a user-defined time period once a new note is activated.
Is there any reason why this shouldn’t be implemented? Please let me know if there is an alternate approach to getting this desired response from my instruments.
You can do the same with Note Off NNA.
Just go to the Instrument Envelopes window, and enable the Volume envelope and Sustain. Then just edit the envelope as you see fit and move the sustain point to where you want it.
And of course switch on Note Off NNA in Instr. Settings.
Thanks for your help… I just figured this out at the same time that you posted. 
Editing the envelope gives you a lot of flexibility here, but it seems like a lot of unnecessary steps when compared to IT’s one-click implementation.
With that said, I’m happy that I can do this in Renoise, but I’d still like to see an easier way to apply it to my instruments.