What to upgrade next?

If you wanted to make an upgrade which would be the next most noticeable improvement. 

1: Power Cord (currently just stock cord)
2: Power tubes (currently JJ's 2 each 300b)
3: Cartridge (currently running Denon 103R)

My system consists of Audion Silver Night Special Edition 300b integrated, Acoustic Solid TT, Zu Soul Superfly speakers with Mission cables. 

Wow Aintitgr8 that makes sense. Maybe that's why I can't hear any difference between the $35 and $750 I.C.'s. I also tried a PS Audio AC12 power cord and there was no difference. The speaker cables I have are Zu Mission with the BU3 connector on the speaker end for a good solid connection. Maybe an upgrade to Zu Event may help or yet another brand of speaker cables. It's so hard to really know what is the bottleneck in the system. 
You already have a very nice system so I am surprised that no one has mentioned room treatments?

Before upgrading anything else, treat the reflection points in your listening space. Put some bass traps in the corners. There are some very simple DIY projects that don’t cost a lot of $$. You want to hang things that can absorb reflections.

I initially stuffed some large bean bag chairs into the corners behind my speakers to see if I could hear a difference (I could). But any large stuffed pillow could work.

As a test, you could also try hanging heavy velour curtains at reflection points to see what kind of effect (sonically) they have.

And play with speaker positioning.
You have to start out getting things good enough that you can hear differences in the things like power cords and tubes. At this point in my reference system changing power cords from one performance level to another is a no brainer to hear the differences. I have to be able to hear the difference between terminations and plugs from one type to another, it's what I do, so I can't help but try to help get someone asking a question like this get on the right track.

An upgrade of speaker cable resolution will allow you to hear interconnect improvements better. The source to preamp is going to make the biggest difference. Keep in mind that as you find cables that improve your system, that there are new levels to get out of further cable improvements. If you think modestly priced cables made a big difference stepping it up from there can make even bigger differences.
Power cables first, and as others have said that will reveal other deficiencies. ...And so it goes. Any effective change will be a revelation, and the next step is a function of what you upgrade first.

After upgrading power cables, my next step was an oversized PS Audio PowerPlant. That made an even more substantial difference. (I already had "good" interconnects, so those got upgraded to very good ones after everything else and now I am done for the time being...)