Try using a compressor. It's a very common misconception that compressors "reduce dynamic range" but this isn't inherently true. Try this: stick a compressor after the amp block and set the attack to something slow like 100ms. Set the ratio high then start playing muted strings on your guitar at, say, quarter notes at around 120bpm; you want to play something staccato that will trigger the compressor then allow it to come back to unity gain. Turn the threshold down until you're getting like 15db of gain reduction. These settings, while not at all musical, will emphasize the fact that a compressor can actually increase dynamic range because you're using the attack settings to make the initial transient loud relative to when leveling is happening. This is what gives lots of tones a characteristic "pop" on recordings in such varied genres as funk, country, and downtuned metal.
From here you can adjust the attack time, knee, and ratio to your liking to sculpt the guitar's transient relative to its sustain. Once you have it where you want it all you have to do is figure out the release so that it doesn't pump aggressively.
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