So as far as the death itself, without checking to refresh my memory, I can recall this much:
He ties himself to a standing stone with his entrails (I'm pretty sure it's his entrails) and dies. Lugaid's men are ordered to shoot the body with a couple of arrows to make sure, then Lugaid triumphantly walks up to the body, possibly to gloat.
When he gets close enough, Cú Chulainn glows with "hero-light" (that's the translation that stands out in my mind the most, I always thought it was a less intense show of power than the riastrad) one last time as his sword falls from his lifeless hand to behead Lugaid. The rest of his men stay back (this may actually be when they shoot the arrows, I'm iffy on the timing of that part) and nobody else approaches Cú Chulainn's body until a corvid lands on his shoulder; I admittedly just saw your post on my dash where someone else mentioned that part - that's why I went with "corvid" - but I already remembered it as being significant. I also remember it being implied (if not said outright) that it's taken as a sign from the Morrígan (or Babd, if the author makes the distinction. You know how it is with na Mórrígna) that he's finally really truly actually dead.
So yeah. That's my recollection, mixed between everything I've read.
So, in BMMM:
Cú Chulainn ties himself to a standing stone so that he might die standing. He ties himself using his "body belt". I think this is a belt and not a euphemism for intestines, mostly because he already yeeted his innards into a lake, and I'm not sure how many of them he's got left at this point.
Cú Chulainn dies
The men of Ireland are afraid to approach him because they think he's still alive.
Erc shames them that they haven't beheaded him yet and they behead him??? This seems like a textual corruption since in the following paragraph it becomes clear that he still has his head, not sure what's going on there.
The Líath Macha comes back and guards Cú Chulainn, killing anyone who approaches him. We are told that he guards CC "as long as his soul was in him and the hero's light from his forehead remained"; presumably the light goes out when he finally actually dies, but that isn't mentioned.
A scald-crow lands on Cú Chulainn's body, making it clear he's dead. There is nothing textual to suggest the bird is anything except a regular carrion bird, but people do tend to read into it.
Lugaid beheads Cú Chulainn (again???) (This one seems to be the actual beheading since it is referenced later)
Cú Chulainn's sword falls from his hand and chops off Lugaid's hand
Cú Chulainn's arm is struck off in revenge
A few small details differ from your account but on the whole it's broadly similar, except that there are no arrows. Arrows are pretty rare in Irish sources, to be honest.
In OCC:
Cú Chulainn asks Láeg to help him go to the standing stone so that the men of Ireland will think him alive and won't behead him. Once there, he just seems to lean against it, I don't think he actually ties himself to it in this one.
Cú Chulainn dies
(Láeg leaves with the Dub Sainglend to go and tell Emer.)
The men of Ireland are afraid to approach Cú Chulainn for three days and three nights (big timeline extension compared to BMMM and very much sets CC up as Rubbish Jesus)
During these three days and nights, Cú Chulainn's body is guarded by the Líath Macha
Medb summons Badb ingen Cailitín and tells her to go and find out whether Cú Chulainn is alive or not.
The men of Ireland see Badb ingen Cailitín in the form of a scald-crow land on Cú Chulainn, so they know he's dead.
They attempt to take Cú Chulainn's sword and it falls and chops off ten of their right hands (? I haven't quite translated this part yet, so that's from eyeballing it) (Later on it seems like one of these hands was Lugaid's, but I'm not sure that was actually specified) ETA having now translated this passage, essentially they can't get close enough because of the sword, so Lugaid suggests they cut the tendon of his hand so that the sword will fall. They do, it does, thirty people lose a hand. (Syntactically: ten kings' sons twenty, hence I misread it as ten originally.) One of them is probably Lugaid but it doesn't actually say so.
Medb tells them to behead Cú Chulainn. They agree it's right for Lugaid to be the one to do this, which he does.
Then Cú Chulainn's head seems to glow? Presumably this is a hero's light situation after death. Again, this is beyond where I've got to in my translation, so while I know the broad outline of what's going on, a few of the finer details are a little vague.
Still no arrows!
I would say your version is closest to Brislech Mór Maige Muirthemne, the earlier text, but this is the one part of the story where they actually largely agree on events with only a few differences, such as Láeg's presence and how much they argue over Cú Chulainn's head before and after it is removed from his body.
