So to be clear as to what you need:
Stream via xsplit @ 720p+
That's pretty much it, right?
I would start in two places. First, the latest System Guide
should target a good set of hardware, even if you don't replace everything. Second, I don't have experience streaming, but I would find out or confirm what taxes your streaming the most. It seems a little odd to me that you're maxed out at low setting, but that could also just be the norm for running xsplit, meaning that a significant hardware upgrade wouldn't necessarily fix your issues.
Before you start buying up hardware, maybe see if you have everything set right in xsplit regarding FPS out, time delays, etc. Just in case.
Save yourself the trouble and don't ask why the TV remote is in the refrigerator.