This is a common complaint made and one of the reasons the Kone has been introduced....to get a better "amp in the room".
A different SS amp will make very little difference, a valve amp might as the power amp imparts some colour ( depending on the amp, gain applied etc).. but...I certainly would not start chasing a Valve amp power amp just yet for various reasons, namely you are adding more variation/colour etc. more gear etc.
The point is the KPA is not a valve amp ( I know, obvious) but doesn't try to be. Its focus is on the whole signal chain so arguably its more geared towards the FOH sound. As a result I have personally focused on that and not got stressed about any lack on Umph as its only for backline - this is a mindset change because the focus was always previously on backline because that was the start of the miked sound. With the KPA this is not the case as you go direct out.
Can you get an amp in the room sound? Yes I think you can but you might need to re-visit your profiles. You are effectively reverse engineering the profile process but removing the cab and mike colour to then put through a real cab.
It does it pretty well and I was always fairly happy with my sound through a guitar cab but you also might need to make more adjustments e.g. use Direct or merged profiles etc,
My comments are very generic of course but I hope that helps in some way...