Let’s take it step by step, shall we?
Voltage
This is critical, because if you go too high, you might destroy your servos or electronics. So good decision to get 7 servos of the same voltage rating 
As a secondary effect, to generate the same power, a higher voltage allows for lower currents, which limits heating. As well as moving the limits in that the motors can move a little faster and with more torque. So generally it is advisable to aim for the highest voltage possible (and available).
Current
This is what actually generates the torque. But more critically, if the power supply runs into its current limit, then the voltage starts to drop, which makes the motors stall. So better choose a solution with more amps than needed and the supply voltage stays more constant. So you are absolutely correct, when you see, that it wouldn’t be an upgrade without a new power supply
If you have a choice between high voltage, but only just enough current, and lower voltage but an abundance of current, I’d choose the latter.
As an aside: Just because the stalling current is 2.3A, doesn’t mean that the motors will actually draw 2.3A each. But it’s a good idea to consider stalling current anyway, so the power-supply doesn’t get overwhelmed in these cases.
Power Supply
These Open Frame Power Supplies need to be wired, yes. They usually have screw terminals on both ends, so soldering shouldn’t be necessary, but you’ll probably have to cut and strip some wires (Just make sure you disconnect them from any power sources like MAINS first before you do… I’ve seen more than someone doing some dangerous stuff)
I would be more worried about how to connect it to your adapter/distribution board. Is it only connected to two of these pin header contacts or is there a different type of connector?
And secondly, these things aren’t water-proof and need a bit of ventilation, so you can’t just stash it into a closed box and have it run hot.
So think about where you’d want to place it, so you don’t accidentally destroy it by either having water or other fluids run into it or it overheating. (The PC Tower for example can be a good place if it doesn’t overcrowd it, there’s still good cooling and there is an outlet).
Ratings and Safety
There’s a lot to be said about how many of these DIY machines have parts that could carry more than they’re rated for. But I’ll just mention one thing: If your Power Supply doesn’t have a fuse, you might want to add one to protect your device looking at those 150W ^^
Power Rating
I don’t know whether anyone has ever measured their power consumption of the SR6. I have only measured my OSR2+Twist with 35kg servos and I did get slightly over 10A @ 7.2V depending on the strokes and axes (i.e. about 75W). But there is a lot of variability: The weight of the case and sleeve, the suction (T-Valve or through the cap and sleeve alone), the friction/lubrication, the stroke range etc. And of course the script. While the SR6 distributes the load more evenly, I think depending on your setup and script it can exceed what an OSR2+Twist takes.
So I can’t give you an exact promise, that the 90W will work in 100% of cases (accounting for losses in the wires and connectors etc.). Yet my intuition and experience would tell me yes, but not by much.
Conclusion
All in all, yes the 6V 15A works, but there isn’t as much margin left and it’s costly.
The open-frame one needs a bit of screwing and management first, but certainly offers more power than you’ll ever need, which is a good thing.
In both cases, think about how you’ll connect the adapter board (which should supply all the servos from my understanding) and consider adding a fuse to avoid some nasty accidents.
Feel free to ask, if there’s anything that’s unclear. Especially if you want to discuss how to connect it to your board. But I’ll need more infos on it to do that.
