Should I upgrade from Sylvania 6DJ8 to better tube

You may get different sound. If you want more detail or a "warmer" sound you can switch. 6DJ8's aren't cheap but run for many many years. They have a great impact on the sound and can be fun to roll. I'd go for Mullards...

Generally Mullards warm, Telefunken neutral, Amperex somewhere in between.

Each brand will 'tailor' the sound somewhat.
Amperex is a nice overall tube, but there are those made in Holland, USA, Japan,etc; they will all have their own characteristics...which makes tube rolling fun.
Some tubes will give a warmer sound, some leaner.

Don't forget the 7308 tubes, which usually provide better highs but not quite as strong bass compared to 6DJ8/6922 tubes.
If you search around you can still find good deals.

In my experience, there is substantial improvement over a 6DJ8 tube by going with a 6922 or 7308 which offer very tight triode sections.

Two top choices are 1960's Siemens 6922 and 1960's US made Amperex 7308 (either orange or white label). The Siemens is very clean, focused and slightly forward and dry, while the Amperex (especially the earlier white label) is holographic, airy, and presents a wonderful midrange. You could hardly go wrong with any of the vintage European tubes...

I am inveterate tube roller. The choice would have been abundantly clear a year ago. In a very short time prices for this family of tubes became insane.
I like the American Amperex nice neutral but musical, The CV2492/3 military Mullards a quiet tube unusually forward and uncolored if you can get the 2493. The 2 is more typically british and warmer. The regular mullard 6922 is very sweet but a little less detailed for my taste. The Siemens is in very broad terms a brighter sounding tube it really depends on which one you end up with there are many "Seimens" . They are all good. I have not had the luxury of hearing the Telefunken.
However as I said they are also all insanely priced or fakes now. I am deeply irritated by the astronomical price increases. Fortunately the tube market has a way of correcting itself so I am waiting before I buy- I need a quad.
The Jan Phillips 6922 is abundant, available and cheap because they were still being made into the 80s. That tube is a bit dry and hard but if your Sylvanias are getting noisy I would swap them out for them until prices cool off. Another alternative are the cheap russian tubes which some people really think are good .In particular the 6N1P I think? I don't care for them and really find the Sovteks et al. to be thin and screechy.
Sorry about being a downer but unless you have a very kind buddy you'll have to dish out serious green.