Start from the beginning.
What is the AR and MR of murder? Did D cause the death and did D intend to cause death or really serious harm? You're quite right that there is no direct intent to murder; only potentially indirect intent. You apply R v Woollin, "Where the charge is murder and in the rare cases where the simple direction is not enough, the jury should be directed that they are not entitled to find the necessary intention, unless they feel sure that death or serious bodily harm was a virtual certainty (barring some unforeseen intervention) as a result of the defendant's actions and that the defendant appreciated that such was the case."
This is a question of fact. You have to make a factual argument about what you think a jury should decide, but ultimately acknowledge that factual questions are determined by the jury.
Then if the offence is made out consider diminished responsibility or insanity. You methodically apply its rules to the situation.
If it's not murder, potentially reduced to involuntary manslaughter, then could it be voluntary manslaughter? Constructive refers to unlawful act that is dangerous and causes death, only mens rea is of the primary unlawful act (battery, ABH); gross is a lawful act which is so negligent as to be criminal, with no mens rea element.
You will want to say, if the jury does not find that there was virtual certainty, and involuntary manslaughter is not made out, that voluntary manslaughter should be considered. This will give you the opportunity to show off to the marker -- even if you think that the jury would find this murder and invol.