Tube rolling experts!!!

I strongly recommend you try a Canadian Westinghouse VU-71 rectifier.  It is a 5U4 rectifier.  This is my favorite of all the 5U4, 5U4GB, GZ34, and 5R4GYS tubes I have tried in my ModWright power supplies.   There is one on sale for $149 on e-bay now, so you can see what I am talking about.  Take a look around and you can probably find one cheaper.  I think highly enough of this tube that I bought 5 of them.  Three are in use and I'm holding 2 as spares.  I have paid anywhere from $99 used to $199 NOS.  I suspect this will be more closely aligned with your stated goals.  I found it to have less of a bright edginess than the Phillips 5R4GYS, but has a nice sweet extended top end with a very sophisticated layering in the midrange.  Brent Jesse has a nice description of these tubes although he has been sold out for years.  They are a well kept secret and getting scarce.

I don't have any experience with the 7DJ8 you are using.  I am using Telefunken 6922's that I got from Upscale.  They are mighty nice tubes, but I can't make a guess how they would compare to your Tungrams.  Enjoy your Elyse!  Dan does nice work.

274b is  a rectifier made specifically for Audio 
The Emmisions lab 274b is a true mesh plate and hand made a fantastic improvement in sound but $275  you power supply needs to be able to handle 3 amps . I use Lundahl transformers in  mine. You can also look up thd Emmisions lab 5u4b also  $275 just look it up and look at thd build quality this true mesh plates produce a much more 3 Dimensional presentation.
I have used several Mullards ,RCA   as well as Shugaung  which the preferred series are actually very hood for under  $35. Best of luck 

I have tried Siemens Cca, Siemens E88CC A frame, Tungsram E88CC, Mullard E88CC Parasol Getter, Tungsram 7DJ8, and Phillips Miniwatt SQ (made in England) in my Modwright Elyse.  I like the Phillips the best, great midrange, great base response, and balanced top end.

Thank you all for your recommendation. I will ordering some of these tubes and try to have some fun! 

I have the Phillips 5R4GYS and Telefunken E88CC's in my Elyse and love the combination.  I did have to send my Elyse back for an issue which was fixed, I included the Telefunkens which Dan compared in his lab, his comment was they are very good.