Basically what I'm looking for are bands that you'd normally classify as Death Metal/Grindcore but certain songs have moments that I feel are very close to something a hardcore band would write. Brutal Truth have moments like this on songs like Ill-Neglect and Dead Smart. Dying Fetus also on albums like Destroy The Opposition and Killing on Adrenaline. I hope I've explained myself well enough to get help because I haven't been able to find other stuff like this myself. Thank you all in advance!

Give these a go, hopefully something to your taste:

Internal Bleeding - probably the most HC influenced of the more well known NYDM bands, Voracious Contempt is my favourite.
Pyrexia - although Sermon of Mockery is their best their mid-period stuff is likely more what you are after try System of the Animal.
Skinless - similar to Dying Fetus, thuggish hc influenced dm with less of the technical dressing.
Dehumanized - Prophecies Foretold is a great record that should be right up your street.
Disciples of Berkowitz - simple fun HC influenced dm, if you dug Skinless you'd probably dig this.
Soils of Fate - Swedish Dying Fetus worship, the Crime Syndicate lp should be exactly what you were after.
Stabwound - see Soils of Fate, basically the same thing.
Banished - Deliver me Unto Pain is a great piece of chugging NYDM
Repudilation - proto-slam with a simple ignorant style in the best possible sense.
Eternal Suffering - crushingly and neanderthal stuff kinda like Hatebreed gone bdm only with fruity gothic undertones, their Drowning in Tragedy album is HEAVY (just ignore the shitty cover at the end)
Vomit Remnants - great Japanese Dying Fetus worship, i'd rec the Indefensible Vehemence and Supreme Entity over their latest.
Blunt Force Trauma - if the name weren't a give away more Japanese DF worship, great stuff though.
Cerebral Hemorrhage (US) - excellent lesser known NYDM.
Revenance - short lived band but their Omen of Tragedy aught to appeal, kinda like Iniquity meets DF.
Crawlspace (Belgium) - Enter the Realm of Chaos is pretty much DM played by a bunch of Belgian hardcore guys.
Gothic - French bdm band, very unreliable but a couple of their releases had a distinctly DF/Soils of Fate vibe.

You could also try some of the more deathly HC releases like:
Eighteen Visions - Yesterday is Time Killed
50 Caliber - Internal Bleeding
Spread the Disease - We Bleed From Many Wounds
and maybe even Racetraitor if you can ignore their cringe worthy politics/white guilt combination

Shroud: Disgorge crossed w/ hardcore or something, only a demo so far though
Venom Prison: NYDM w/ female hardcore vox, some anti misogyny theme going on here as well
Gatecreeper: HM2/Swedeath meets modern hardcore, plus they tour w/ Nails if that counts
Carnal Decay: Groove of bdm, simple songwriting/tough guy vox of hardcore
Pit of Toxic Slime: More thuggish slammy NYDM

http://www.BlameGodUSA.bandcamp.com

Grind/PV with a tinge of death metal with some HC mosh parts.