Congratulations on the WA6-SE gen 1. I have the same amp. With the right tubes it can be really something special.
In regards to your questions...
1. You're absolutely right. Tube stocks of high quality NOS tubes are slowly drying up. They are available but you'll usually have to set aside more of a budget.
2. On the WA6-SE gen 1 you can really achieve more of the tubey sound you seek by rolling the rectifier. It sounds like you and I have similar taste in sound signatures. I've rolled at least 8-10 different rectifiers in the WA6-SE and in my opinion the rectifier that gave me the most tubey sound without being rolled off on the top and bottom frequencies has been the GEC/Osram U52. This is in the 5U4G family. It's considered to be a quintessential example of the classic British Hi-Fi sound. It's got an excellent organic mid range and does absolutely amazing things to vocals. It has a beautiful holographic 3-D soundstage and adds that warmth you seek. The real issue with these tubes is price. They are expensive! You can find true NOS examples for between $400-$650.00. Very expensive but these really one of the holy grail tubes. Some of the other British rectifiers will in part, get you to the level of the U52 but not totally. Some of the Brimar rectifiers in the 5U4G family are very good. Maybe not to the level of the U52 but still very good. These tubes will also come with a more reasonable price. So this is always something to consider.
I recommend reading this thread on rectifiers. I've tried most on this list and agree with almost every point made. I personally didn't like the Western Electric that is highlighted here as the best in the 5U4G family. But other than that I think this list is spot on.
https://www.head-fi.org/threads/dub...mparison-rectifer-tube-rolling-thread.694525/
In terms of the 6DE7'S...I'd actually recommend going with the Toshiba 6DE7's that Woo Audio sells. They are also very pricey but really the best of the best. I have a great deal of respect for the extensive screening that Woo Audio does in selecting the NOS tubes that they sell. They go through hundreds of tubes to weed out the underperforming tubes. When you buy a matched pair they are within very tight tolerances. You can actually hear the quality. So again for the 6DE7's I'd absolutely go with Woo Audio.
Anyway hope this helps. Let us know what you decide. Happy listening!