well, i hate to tell you, but this is going to be a battle not easily won.
simply put, you have an almost exclusively digital effects chain and you're trying to achieve a tone that is only achieved via analog signal paths. meaning - valves/tubes. it will be near impossible to get the tone that you're looking for with the gear that you're working with... not saying that it's impossible, but very difficult nonetheless.
Not super familiar with that pedal but from what i see you're going to want to turn the compressor down or off... and probably the noise suppressor as well. With active EMG pickups in your guitar you shouldn't really need to apply a noise gate at all. this is a serious tone sucker becuase it's effecting the attack that the release of the notes you play. from there you can dial in a distortion and see how that feels...
in a perfect world, this is what i would do:
lose the EMG pickups, high output pickups are great for distorted tones and they really scream - but they lack dynamics. Update your pedal... probably not what you were wanting to hear but it will do the most for your tone... Vox makes a nice little unit that actually has a tube in it to simulate the valve dynamics... could be your best answer.