Wow - still a bit tricky to understand your issue. `your guitar processor connects to the computer, which I guess is 'the box' - not s term we use that much in the UK.
"Better amplified sound?" You mean you want it to sound like it's come out of a guitar cab? That I get. In all honesty, simulating the subtle effects of an actual loudspeaker cone in a box mean that the real solutions are probably mainly EQ based with perhaps a touch of compression, and maybe very subtle distortion. More than that is processing as an effect, and your VG has more adjustment of these than trying to do it in the computer. After all, all the work done by the processor to reproduce individual amps and guitars is more sophisticated that normal eq. I'm guessing but I suspect that to you, it just doesn't sound like it does used live? So it's your stage amp, or the DI'd sound getting to your ears with the room sound imprinted onto it. A bit of delay, a bit of reverb, a simulation of spill?
Can you give us a run down on what the problem is you want to solve - it's still not very clear. It sounds to my ears just a bit thin. Maybe your eq is just to savage for the clean sound, leaving it thin with no body. It's also very dry, so something to make it sound like it's in a space and not just a dead DI would help?
Latency of under 10mS is usually OK. Mines 8.9 and I can work happily with that and it doesn't bother me. It's the equivalent of having your amp 8 feet or so away from you.