Hey man, I'm using Bias FX 2 with Bias Amp tonematch. Guitar is still the a-600 with hz h2 + je-1000.
I made a quick YT video with a pic of my EQ settings. First one is without any EQ and is closest to the original HCDR tone. Second one is with a high cut and 3rd one is with the EQ setting you see in the pic. I really like the last one but with those settings, the tone is too weak and not as good as it should be withput any EQ. Each track is around 1min 10s or so...
I think the first one, like you said sounds the closest to that HCDR album tone but I do notice the harshness a little, but I think that's just inherent to the tone. The second one is pretty good as well but it lacks a little bit of the clarity I think. Still very good though. Honestly it would probably be the one for sitting in a mix though. The 3rd one doesn't sound bad either, just a little quieter than the others. I didn't like it upon first listen but it's actually growing on me upon more listens. It sounds excellent for the lead sections, but the low end sounds a little flubby.
I haven't messed with the Bias FX a whole lot. I think overall your tone sounds really good but I too notice the things you mention. Have you thought of throwing a noise gate or compressor anywhere in the path? Mostly for the first one you showed. I think that one is really good but the hiss is noticable.
I didn't think about it until listening to the clips a few times but another thing to note is that while you're achieving basically the tone you would on the actual recordings I would imagine that these songs were at the very least double tracked or something. Maybe not the leads, but I've never really looked into that. Your lead tone sounds very good so I wouldn't worry about that too much. To my ears it sounds like it could use a little bit more low end in some places, but on the open notes on the low E string it has the perfect percussiveness. One problem we all have as guitar players is that when we're trying to emulate someone's tone we're often not taking into consideration multi-tracking, post processing, etc, and then we may have a great tone for the room but is awful in a mix. I had a guy from a band I really liked point out this same issue to me years ago when I was asking him for tips and it's helped me a lot in the recording department if that's what you're after.
What he advised was that I set my gain to where I have just the right amount to sound out my harmonics/pinch harmonics without them sounding choked out. Next I rolled back a lot of my EQ. For years I'd done the things I'd learned from here back in the day with low-end around 12:00, and Mid and Treble around 3:00. This sounded great to me for a while but after a bit it became too abrasive to my ears. What was suggested to me though was that I set each of these frequencies to around 12:00 and make very minor adjustments from there. It sounded odd to me at first but it makes sense as it's allowing the guitar to sit where it belongs in a mix more, and allows the bass to do it's job a bit.
All in all, I wouldn't worry about it too much but I know as a guitar player that it's often hard to let something like this go once you notice it. I know it may be a big pain in the ass but perhaps roll off the gain just a small amount and then try doing some recordings multi-tracked to see how it sounds in layers. I imagine your just using the BIAS FX into your DAW so this is probably much easier to do than having to mic things up and whatnot. If you have a bass also try to record a bassline under it to see if that helps.
As much as I love Alexi's tone on Hatebreeder, for example, his tone on it's own is somewhat thin in some areas. The intro riff to Downfall has that emaculate percussive sound, which is great, but some of the leads can sound somewhat nasally on other songs. Were it not for the heavily distorted bass underneath a lot of these songs I'd imagine the guitar tone would be a lot less enjoyable.
I personally really love the tone on Are You Dead Yet the most and I'm doing a build aiming for it at the moment. Something about it just sounds so perfectly full in all the right ways to me, and I think that setup he had at the time sounded even better live.
TL;DR, your tone sounds great on it's own but in the context of recording it probably just needs mixed in with other instruments.