Nice preamp. Try to invest in some Siemens or Tele ECC83, it should make it a bit better, and if NOS should last forever. Also a very good match for RWS (I do have it too). I'd just try some other SUTs, but that is more of the personal preference, or acquired taste. Like herbs and spices, like Syrah vs Shiraz...
Your speakers have a low sensitivity, but also unkind impedance curve, which makes for a legitimate double whammy... If you want to drive them properly, something based on KT120 - better yet, KT150 - and at least 100 wpch, would work for sure. ARC is good, but that will costs much more than your budget dictates. Heck, retubing them big monoblocks might cost as much...
I tried to drive Dynaudio S40 with Audiomat, which is 30 wpch and amp known for great current. However, it was not enough to control LF. When pushed, amp lose the control over the LF drivers and they would start farting... If pushed just a bit more, drivers would bottom out and fart out their last fart. Lil' Bel Canto S300iU I had handy sounded "better" than Audiomat... Now, if hooked up to higher sensitivity speakers with tame impedance curve, Audiomat far surpasses Bel Canto.
Simply, EL34, 6L6, KT60, KT77, even KT88 - based designs are not enough for your speakers.
When amp and speakers are not properly matched, that distortion is always present. Most of the time, people who are listening at low levels would not even know that something is wrong. However, if they would change the amp, suddenly a mediocre SS would sound noticeably better than a great tube amp... And they would blame the tubes.
If you want to experience the tubes, I would suggest buying a nice used tube amp and above mentioned (also used) Tannoys - if you can find 15" dual concentric, thats where the magic happens. Then hook up both speakers, changing back and forth for some time. Give the tubes / Tannoys some time before you decide what is better.
Did I say you have a very nice cartridge?