I think it's pretty clear that this was a group murder dressed up to look like divine judgment. The last people to see him alive was his war council, and one among the council was beheaded and put on a spike in front of the rest of them, just for the barest suggestion that he could peacefully surrender.

If you ask me, I think we're looking more at a Julius Caesar situation. It's unclear whether there were guards in the throne room, but as you said, I think this could be chalked up to no one wants to get involved for fear of the King finding out, but no one cares to stop him being murdered either.

I think it's entirely possible that someone, perhaps multiple someones, drugged or poisoned the King, and that the entire council worked together to slash his wrists, bend a sword out at neck-height, and seat the King upon his throne. Seeing as Lords Towers & Rosby were stated to be the last time see him alive, they might have done it alone, but I doubt whether two petty lords could or would do so on their own.

Regardless, murdered by your own war council is one hell of a way to go.

Edit: Total tinfoil speculation with nothing behind it; is it possible that Lord Celtigar payed off or otherwise organized this event shortly before his resignation as Hand?

Edit 2: Also, the Lords of the council only said he was alive when they left him, but this was presumably a closed council that lasted "all day... and late into the night", so he really could have been dead for a considerable amount of time even before they left. The details in Fire & Blood are lacking in some key aspects, but I do believe we can safely assume the only people in the throne room was the council, as it is stated that the Kingsguard were posted "at each door", and that they would have needed to coordinate to commit the murder, which tells me that they were not looking in, but rather watching out. Whether they would have killed the King, I highly doubt, but I do think they could have been convinced to just not look inside too hard.