I was compelled to post by that list of bands, we could be friends.
Any of the C-Pig, C-Bomb, Aftermath or Painkiller can totally do older Converge/Coalesce, Botch, etc. Just depends on your preference. I can't comment on the others, never had them. For The Saddest Day sound specifically you'd want a PK.
The amp is the important part. I would look for a 5150/6505, a TS type OD, and a good 4x12, if you're serious. The + is a slightly different sounding amp, the lead channel is more high mid oriented and brighter. The standard model (non+) has more low mid grind, and is usually the preferred version for this type of thing. Try them both if you can.
Combos are for choads.
Ballou used an 81 into a Metalzone (lol) into a JMP and a V4 back in the day. So there's any number of ways to get there, just keep that in mind.
For the sludgedoom thing, use a PAF or P90-ish neck pickup, roll the tone knob down a bit, and play really loud. You won't get a V4/Model T thing out of a 5150, but you can get real good sludgedoom sounds, and if you can't, get a fuzz and run on the clean channel. A-Pig is awesome for this sort of thing.