I did, that's how I got that it's the 2-5-1 (if you play the E major chord). And, a 2-5-1 within a key NEVER sounds bad.

And, you've NEVER heard a cat play a substitute chord at the end of a progression?
No way? 
Here is a post I did a while back that does that very thing. I think that it is a little different situation than what we are talking about, but it still works. This is Lord I lift your name on high and you actually modulate to E from Db in the middle of the verse and back down to start the verse again. It's written for organ, but you can see where it's going.
In the key of Db
BP/LH/RH
Db/F-Bb/Eb-Ab-Db Lord, I
Gb/F-Ab-Bb/F-Ab-Db lift Your name on
Ab/Gb-Ab-Db-Eb/Gb-Bb-Db High
Ab/Gb-A-C/F-A-C
Db/F-Bb/Eb-Ab-Db Lord, I
Gb/F-Ab-Bb/F-Ab-Db love to sing Your
Ab/Gb-Ab-Db-Eb/Gb-Bb-Db praises
Gb/Ab-A-Db/A-Db-E
B/A-B-Eb/Gb-B-Eb
E/G#-C#/F#-B-E I'm so (yes, you just modulated to E)
A/G#-A-C#/G#-B-E glad Your in my
B/A-C#-E-F#/A-C#-E life
B/A-C-D#/G#-C-D#
E/G#-C#/F#-B-E I'm so
A/G#-A-C#/G#-B-E glad You came to
B/A-C#-E-F#/A-C#-E save us
Ab/Gb-Ab-Bb/Db-F-Ab (Back to Db we go)
repeat or go on to chorus
Db/F-Bb/Eb-Ab-Db You came from
Db/F-Gb-Bb-Db/F-Ab-Db Heaven to
Db/G-Ab-C-Eb/G-Bb-Eb Earth to
Db/A-Db-Eb/Gb-Ab-Db show the
Db/F-Bb/Eb-Ab-Db way
Ab/Gb-A-C/F-A-C
Db/F-Bb/Eb-Ab-Db From the
Db/F-Gb-Bb-Db/F-Ab-Db Earth to the
Db/G-Ab-C-Eb/G-Bb-Eb Cross my
C/E-Bb/D-Gb-A debt
F/Eb-A/Db-F-Ab to
Bb/D-F-A/C-F-A pay
Eb/F-Gb-Bb-Db/F-Ab-Db From the cross to the
Ab/Gb-Ab-Bb/Db-F-Ab grave, from the
F/Eb-G-Bb-D/F-Bb-D-F grave
F/A-Db-Eb-Gb/Ab-Db-F to the
Bb/Ab-C-Db-F/Ab-C-Eb sky. Lord, I
Eb/F-Gb-Bb-Db/Gb-Bb-Db lift Your
Ab/Gb-A-C/F-A-C name on
Db/F-Bb/Eb-Ab-Db high