How do I get a thick but crisp guitar track with the Tascam DP-24?

I’ve been a musician all my life but I am fairly new to home recording. I have quality mics, amps, & instruments, however right now I am having to use one of my spare bedrooms as my recording space. I am using the Tascam DP-24 for all of my tracking. I haven’t had any luck with micing my guitar amp, there’s always way too much bleed through & the distortion is very muddy. So I have started just running straight from my multi-processor into my mixer then from the mixer into the dp-24. I think I’ve been scooping out all the mids correctly, but I could be wrong. My main problem is tone. I want a very heavy but crisp tone but no matter how much tweeking I do on the pedal & on the dp-24s mixer the tone is still muddy. An example of the thick but punchy sound I’m after would be the guitar tone from The Great Southern Trend Kill. Any advice on how to generate & capture this tone would be greatly appreciated.