Do vacuum tube test values reflect sound quality?

There is no test that correlates with sound quality except you want transconductance to be well within the good range and the two sections of a 6SN7 or any dual triode to be about equal in transconductance, but for two tubes that test well, no measurement is going to tell you that one sounds better than the other. Furthermore, with octal triodes you need to be aware of microphonics. Some are very sensitive and THAT can color the sound.

@lewm  Thank you.

So, would it be better if the 3000 and 2750 values were more closely matched?  The two tubes match each other closely which I assume is good. 

Have you heard differences between tube brands thru THAT unit?

I would listen to the ones I bought, AFTER I break them in for 60 hours by simply leaving the unit on, no signal required, and if they sound great, expect many years of life.

IF they don't sound great, try a different tube not the same one, no matter what it measures.

Sound good, but not better than prior good ones, there's your 'never without music spares', find some that you prefer some day. 

Keep in mind, each time we push pins in a socket; rotate a dial; move a switch on a tube tester, it's similar but can be slightly/perceptibly different; and published numbers from two separate testers are not scientifically exact.

If you had your own tester, then you could test them when received, and every 6 months, keep a chart, have confidence in your tubes when problems occur. 

@elliottbnewcombjr I've tried several different input tubes as well as output tubes.  I can hear noticeable differences.  I'm pretty set on Telefunken ECC801S for input tubes.  Siemens ECC801S being a close second.  

I hadn't tried very many different output tubes until recently.  I now have a couple of pairs that work well.  I just thought I'd try something different for grins.   

These days, for the exotic types and brands you mention (Siemens and TFK), I’d hazard a guess that there are more fakes than real ones on the market. I’d stay away from eBay as a source for such tubes. Most reputable dealers don’t pretend to have such tubes to sell. I assume you know that “ECC801”indicates a selected ECC81, even more rare than the run of the mill version of Siemens or TFK. What few exotic small signal triodes that I own I bought in the 1970s, so I know they are for real at least. However, maybe you are an expert in examining these tubes to prove to yourself that they are what they say they are. I certainly am not, even after 45 years in this hobby. To the question you did ask, yes I think 3000 and 2750 are sufficiently well matched sections.