If you want to spend more money, get a better frame. Don't get me wrong, the LHT is good value for the money. But long chainstays and plain bottom bracket shell using cheap steel add up to a lot of flex.
That is annoying. But when you show up wanting speed... that set off alarm bells in my head. It will NEVER be fast. If you want to keep the price equivalent, try an aluminum touring bike or a cross bike like the Bianchi Axis.
But you want to be looking at other frames, IMHO.
Btw, touring bikes are made to be tough and comfy. I test rode a Waterford Adventure cycle with XT components once. It took a looong time to accelerate.
It had no appreciable BB flex, it was big and heavy and speed was just not on the agenda when they made it. Great touring bike.
So you have some decisions to make. But the first one is the type of frame you want.