Will Step Up Transformer Improve the Sound Quality?

A SUT adds an extra interconnect, and extra connections, into the most sensitive signal path in all of audio. That's not to say it can't be an improvement. Some guys swear by them. Some even go so far as to say all cartridges benefit from a step up. In general though I think unless it is a very low output cartridge then the odds are about equal to screw it up as make it better.

Your cart at 0.3mV is a little on the low side for me personally, but nowhere near to where a SUT starts to feel real necessary. 

Even if it is, consider the big picture. Spend a grand on a SUT, another $500 or so on a good interconnect, for what? To make a $1350 cartridge sound a little better? Maybe? For $60 you could buy a sheet of fO.q tape, guaranteed to make it sound better. Synergistic PHT, Townshend Pods, stuff like that costs a little more but still way less than the SUT and way more likely to make a satisfyingly big improvement. Way more. 

Look at it this way. I have never in my life messed with a SUT- and if you heard my rig your jaw would drop. So I rather doubt a SUT is the way to go.

For future reference, I find it a whole lot easier to avoid low output cartridges. Just like it makes life a whole lot easier to avoid low sensitivity speakers. Medium output cart, lots and lots of great phono stages. No problem. Down below .3mV, choices rapidly disappear, while price tags rapidly escalate. I prefer to not make things harder than they need to be.

You can buy and try a Bellari MT-502 SUT ($499) and an AQ Silver Extreme IC ($90 from HCM). I use this combination! I prefer it over a high-gain phono stage. 

Thank you for the great feedback.  I did not perceive an issue with the sound of my system.  I just wanted to get this forum's opinion on whether this was a worthwhile enhancement.  mijostyn thanks for the other insights on my system.  I am content with the bass but what is your advice on the REL's - is it a tweak or are you saying that the crossover issue is inherent with the REL's.  

IF you already have a MM Phono stage you really like, then a SUT simply boosts signal strength to keep on using that MM Phono stage. That's the choice I made, very happy results.

SUTs have their own problems.  They add distortions, though different from active stages.  They can also pick up hum.  This in addition to extra cables and connections mentioned above.

They also must be matched properly to the cartridge, not only for gain but for primary impedance (load that the cartridge sees).

I have a Supex cartridge and a matching sdt-722 transformer that sounded better than the active stage I had at the time, but the same transformer did not sound as good as the active stage with similarly spec'd Audioquest and Lyra cartridges.

YMMV