I've heard bad things about the Pro-Ject, it's going to basically be a CMOY inside and the K701s do not take kindly to low end amps. Either invest in a more substantial setup, maybe an Audio-Gd compass, M3, or tube amp, or pick different headphones.
Tube rolling is not equivalent to EQ'ing which is intentionally amplifying/cutting amplitude on certain frequency ranges. Tube rolling is more like changing parts inside an amplifier, like different caps, resistors, entirely different circuits - it is changing the whole fingerprint of the sound not just twiddling with specific frequency ranges. There is no one way that the music was "intended to sound" since the sound is just a source recording being represented 10000 different ways by various audio component setups, and changing tubes again is just like turning your amp into a different amplifier, but EQing your music is changing music at the source level which is not natural.
I would not trust Stereophile's opinions on anything, they're written some pretty goofy stuff when it comes to headphone related reviews. Their experience is mostly in home audio stuff, and they admit this openly in their reviews - every time they do something with headphones they mention that they're sorta new to headphones. I'd trust headfi above all as some people on this site have listened to EVERYTHING vs. stereophile which is just going to say 'Boy this sounds great' plugging in the latest designer $800 amp from some big name mainstream hifi company just getting into headphone products packing a CMOY inside a fancy case.
I don't really think anything from Beyerdynamic is a good first headphone. They displease a lot of people, their treble is extremely forward in the Home models and the Pro ones are famous for their ghetto bass - it's tricky to get them to sound the way you like, although I still enjoy mine they are a shock compared to my HD650s. I think HD650s with a good headphone cable can beat anything, even my newly recabled K702s, rewired with Mundorf silver/gold the HD650s have the most relaxing, pleasing sound without overemphasis of anything - I know what I like and HD650s are it. Some people like the up front sound of Grado and Beyer and that's their decision, I enjoy hearing the differences between various headphones but it's going to take a lot to dethrone my HD650s. While they are notoriously tough to amplify right, this really just means that they are a limitless canvas upon which to spend money and no gear is too good for them - they sound decent enough even on cheaper gear and only get better the more you spend - and I think they have a very safe sound signature that a lot of people will like, although some might be disappointed by their restrained sound on cheap gear with the stock cable. When you recable and add serious amps and sources, they will wtfpwn you.