Optimizing the Prima Luna Premium Integrated amp

You might want to try the Amperex Holland 12AU7s. Be careful though as they were sometimes "only" rebranded Mullards, you can tell by the etched code. My all time favorite in any position is the direct sub 7316 an Amperex product but now very expensive,
It really sounds like a German tube such as a Telefunken would do the trick. Also you can call Upscale for help since they import Prima Luna they will know what works to bring out the qualities you want.

I have swapped a number of NOS 12au7 in my Primaluna Dialogue One with great success. To my ears the Amperex Bugle Boys are the best. I have failed in my quest for a "reasonably" priced 7316 Amperex mentioned by Mechans above. I also like the RCA Clear Tops Side Getter, the Psvane Shuguang Black Treasure. Frankly, the Mullards were not as clear as the tubes above.

You should also try swapping out the 12ax7 for some Sylvania 5751 Triple Mica black plate and or/grey plate.

Another suggestion, try the NOS Russian Reflector 6n3ce output tube (6L6). This combo of tubes bring this integrated to a whole new level, much, much better.

If 5751s are suitable for this amp then you must try them in place of the 12AX7s. I am an inveterate tube roller and find switching the tube to be the fastest easiest mod you can do yourself. Most amps will tolerate changes to the smal signal tubes, if the pinout is the same.
There are a bunch of good 5751s to try but most everyone wants the "holy Grail"- the late 50s NOS triple mica black plate by Sylvania. I use them and they are truly great, but less rare 5751s work out pretty dammned well, try the RCA white print or Command series, GE are abundantand cheap. a decent place to start, try to get their 5 Star Black Plates, The rarest of the rare are Raytheon windmill getters. They are worth the trouble but very expensive and truly rare, unlike every tube you see on ebetrade. If you just want to dip a toe in the 5751 water the JAN tubes can still be had NOS but watch out as some pretend it is the late 50s early 60s tube. Check the Audio Asylum Trader section lots of reasonably priced tubes for sale, if you can't find what you want here.

for the Premium integrated the manufacturer tube configuration is all 12AU7's. I have swapped in some Amperex 12AT7's and Jan Phillips 12AX7WA's, in both cases
the Mullard 12AU7's were better in the front sockets. Toying with shelling out for some Seimens Nickel plate 12AU7/ECC82's.

All 12AU7s is the manufacturers tube designation for the amp we are discussing. In that event the OP may want to try another direct sub the 5814. The 50s Hytron and later CBS Hytrons are held in high esteem but it is necesarry to them alone to get a feel for the tuybe type. It has what I call the "strong, clean signal" that I find desirable in certain situations.
The RCA 5814 versions are very good and as are many others, try em they shouldn't cost a lot. The other clean strong signal 12AU7 I have some experience with is the Brimar 13D5 which has been around for a few years, but not sure who is selling them now.
As I said earlier if you can find some good Telefunken ECC82s even used testing good you may want to try them. Lets face it most of what is called NOS is just OS and not new.
I don't have a great deal of faith in the RCA 12AU7 clear tops , from personal experience which I admit was a gift of some decent and some unusuable tubes I got in a batch. I don't know much about the others, try Brent Jessies Audiotubes web site, he has some details on the US types. I settled on 7316s a while ago as my 12AU7 of choice and have been hunting them until recently now that prices are really too high for most people. On E Betrade people list them with singles foe $100 and up to start for single tubes. I can't recommend anyone try them at that price.
Current production has gotten much better from all over. My old Pal Joe imports some of the Chinese tubes which he has great faith in. Others have admired the new Gold Lion smasll signal tubes with many other New Sensor tubes.
The 5814s when I last looked were still reasonable, I think the Brimar 13D(X) tubes have gotten a bit more expensive and Teles while Desirable are plentiful as pulls and hit and miss on price. IMHO YMMV etc. etc.