Question for tube aficionados

I have a vintage Conrad-Johnson PV 11 preamp.
 I’ve always re-tubed it  with the cheapest tubes from Tube Depot (e.g. Electro-Harmonix 12AU7 and 12AX7, Sovtek 5751 and the like.). I’ve been very happy with the sound.
 My question is:
 Would it be worthwhile to spend more money on more exotic tubes?
  Would there be any appreciable difference in the sound?
 I’m powering the system with NuForce Reference 9 V3 monoblocks.
Having tube rolled integrated amps, phono stages, and amplifiers, I can say that tubes can make all the difference in terms of gain, clarity and other aspects. The tubes in your CJ pre will make the most difference. I replaced the stock 12ax7 tubes in my pre with GE 5751 tubes and it made an incredible difference in terms of clarity, gain, presence, and soundstage. Those tubes were $60 each, but it was an immeasurable investment.

But I also did my research in terms of what tubes were the most complementary to my unit beforehand.

@hedgehog gives good advice above about how and when to replace tubes: line stage first, then phono section, and make mental notes of the sound changes as you progress.

1. Line stage: 2 x 12AU7: I’m assuming
2. Phono: 1 x 5751 and 3 x 12AX7

12AU7s: Lots of good opportunities here.
The NOS Mullards are end stage tubes for many, meaning once you hear it, you never let go of the tubes. I bought 4 matched of these tubes for about $125 each after shipping, taxes, matching, etc. from Upscale last year to try in my PrimaLuna tube integrated. I also needed a softer top end b/c I have ribbon tweeters in my speakers, which can burn your ears with more aggressive tube profiles.

The Mullards (specifically the M8136 model from Upscale) are expensive, yes, but everything they said was true: softened but very beautiful top end slightly rolled off. The soundstage is to do for, it puts the band in the room with you. Not many cons to this tube other than a slightly rolled off bottom end. RV, I think this would be an obvious choice for you.

The NOS Brimars are excellent too at $80 each, I have a pair, BUT it does not offer the softened top end you are looking for.

The RADIOTECHNIQUE 12AU7s: for $95 each, have not tried, but probably excellent+.

there are other NOS tubes out there. I recommend going to Upscale website, and watching the videos on each tube that they sell.

 I will soon have a credit of about $130 from Tube Depot, having already bought but not opened, a complete set of tubes for my preamp.
With this, I’m thinking of getting two Gold Lion 12AU 7’s for my line section.
This won’t cost me anything extra. If this doesn’t make much difference I’ll go to more expensive NOS tubes (of which Tube Depot has a limited supply.)
I mentioned the 6SN7GTBs as between my preamp (Schiit Freya) and my amp (Dennis Had Firebottle HO) that's all there is for non power or rectifier tubes. My previous amp used 12AX7s and 12AT7s with my preference winding up as new Gold Lions for the 12AX7s and NOS Mullards for the 12AT7s.
Pretty simple, really.  Better tubes equal better sound.

For these variants, with few exceptions, you need to look toward old production.  Not necessarily NOS, though so many aspire to that.  I found you can do VERY well for yourself buying tubes others sneer at as they come up measuring as having obviously miles on their clocks.  Old tubes often play quite a long time, and pretty much sound great until they give out.

As has been mentioned the best 12AX7 tubes are 5751.  What I can add is the best 12AU7 are 7316.  Both tubes will cost you deep in the purse.  Both tubes instantly convince you that you won't go back.

If you do want to buy new production tubes, Shuguang triple mica 12AX7B aka Silver Dragon and Psvane 12AX7 and 12AU7 stack up surprisingly well