No, I haven't tried them in this amp.  But, I did go back and forth between the original 6V6's and 6L6's in my Brownnote D'Lite.  In that case, I was going from a 6V6 optomized circuit to 6L6. 

Just a heads-up (for everyone thinking of trying this) about swapping.  I haven't taken a close look at Nik's OT for the Overtone but I'm guessing it doesn't have dual Primaries....I'll check when I get home.  The pair of 6L6's want to see a primary impedance of around 5K and conversely a pair of 6V6's...8K.  Therefore, it isn't a simple case of re-bias and play.  You have an impedance mismatch BUT because there are 4,8, and 16 ohm secondary taps there is leeway to better approximate the correct primary impedance. 

On the D'lite you have an 8K Pri OT  (6V6) that you want to "knock down" to 4 or 5K for 6L6's.  To do so just re-label the secondaries as 2, 4 and 8 ohms instead of 4,8, and 16.  I'm certainly no EE so correct me if my logic is wrong but 6L6 to 6V6 should be the opposite....8, 16, and 32 ohm instead of 4, 8, and 16.   All this being said, a 100% impedance mis-match can sound great and the OT should be able to handle it. 

Discuss.... 

 I am wondering if Nik could build this for 6V6, maybe using the OT/ PT from a Blackface or 5E3 Deluxe ?

You can swap 6v6s for 6L6s as long as you adjust the bias. The impedance mismatch doesn't amount to much. I use 6v6s in my ots with switched/ fixed cathode bias (500ohms/10 watts) and it sounds great. I've done this swap with Bassmans, Twins, Bandmasters, a Blues Deluxe, and I've even run them in my Super Twin. As long as you get the bias half way close you'll be fine. Try it! Use good quality tubes that can handle the voltage. My Deluxe Reverb runs the plates at about 420 volts DC. you don't want to go much higher than that so I hear. i've run 6v6s (JJs) at 440v all night however, and nothing happened.