[RobW]

We run combat according to the Advanced Melee rules, which are clear on this question.

1. Initiating HTH is an action available for any figure moving 1/2 MA or less**. This includes engaged figures who can only shift.
2. The move onto the defender's hex happens during the movement phase.
3. As the attacker moves onto the defender hex, it drops any non-HTH weapons and shield in the hex it entered from.
4. The defender then rolls to see if they repel the attack, get their dagger ready, etc.
5. If the attack is repelled, the attacker return to the entry hex but without its weapon/shield, now laying there on the ground.
6. If the attack is not repelled, the attacker and defender go down in the defender's hex.
7. In any case, the attacker has used their action for the turn.

So to answer the OP's question, the attempt to initiate HTH is resolved during the movement phase (alternative 1).

** given the restrictions, ie attacker has higher MA OR defender backed against a wall, prone, or kneeling OR attacker enters from rear OR defender agrees