Looking for a hardware sequencer with the following features. What gets me closest?
A4? 
Oxi One Exactly
Yep oxi one, polyend play, torso t1 (?)
Squarp Pyramid
Check out the Torso T1. I love it 
I have been searching for a sequencer with the capabilities you mentioned. Have tried plugins, bought a NDLR, did loads of research and have eventually settled on the T1.
It does all the things you want and a few more. Itās super compact, very playable and performative. The Cycles feature, for example, is suuuuper powerful.
Iād highly recommend watching some YouTubez and checking out the āNauts T1 thread and perhaps the T1 Discord before dropping any money.
)What about the squid?
Are you sure T-1 does this @nooooddy? I didnāt remember it like this from when I had it but of course I can be wrong
midibox sequencer
If Iām understanding the āindependent triggering of sequences per channelā correct:
The T1 has 16 channels, each of which contains a different sequence. At any time you can mute, unmute any channel and therefore independently control sequences per channel.
The Temp command, Channel command and midi routing command can all be used in conjunction with things like pulses and step length to mess with triggering further.
So for example, rather than just muting a kick track you could use the Temp command to temporarily reduce Pulses to 0, effectively stopping triggers to the kick, let the beat breatheā¦. Then twist the Pulses knob, drop a shit load of kicks and let go of the Temp button to return to the original beat, having briefly created a rhythmic variation in an interesting and performative way 
Deluge
That indeed already a lot.
The OP might also be interested in how Ableton clips in Session view can be played. So where on one track/channel you already jump ahead to the next clip whilst the other clips are still on the row above.
That is not possible on T-1 as far as I know right? For that a Hapax is perfect. Oxi also does that, albeit a bit less clear than the Hapax (in my opinion).
Definitely Five12 Vector with a Launchpad Mini
Oxi is the one. Does all you mentioned and much more.
You can put 8 drum tracks in one sequencer track, so you have still have the three other sequencer tracks available for chords/generative/mono.
You can even use all 4 sequencers for drums or monophonic stuff, so 32 lanes in total.
I love it. Also because it has tons of modulation options.
What I want to be able to do is to switch out a channelās sequence independent of the others. So say I have a kick pattern playing, I want to be able to change that pattern whilst the others continue (just like ableton live clip behaviour). I find this behaviour ideal for live performance.
I use the Nerdseq. Ticks all the boxes you mentioned.
Can be used for Midi only aswell
Hapax would be my recommendation. I think the tough choice here is deciding if you want a sound/sample engine paired with the sequencer. Not sure how the rest of your setup looks like but IMO thereās something nice about having a dedicated sequencer that only does that and stays central to everything else.
I really like the nerdseq but I think itās a bit less ergonomic and you have to like tracker style sequencing that can be a bit grueling (but very rewarding)
I would have just gotten a cirklon and been done with it, but i have neither the patience to wait year(s) or pay markup on secondary market for one.
everything else mentioned here would do the trick as well, but you have to really pick one that suits your I/O and ergonomic needs relative to the rest of your gears
Another vote for the Hapax here.
Incredibly deep yet amazingly simpleā¦ and itās got even better since the 2.0 update.
Itās still missing a couple of things I want, but thereās nothing to match it as a studio centrepiece.
Following the Reliq with interest thoughā¦
Of those recommended, which would you say is the best for improvising? My goal is to use the sequencer to control the 4 channels of the Pulsar and improvise live techno.
Generally I would suggest to check out what I call a āmatrix sequencerā, because those are pretty efficient to work with in a live situation and we can quickly change between modes to improvise with notes, clips, and song-structure.
From the above mentioned sequencers, this would be the OXI One.
I use it for live-performance-composing ā¦ 
if that makes any sense.