Initiative is not the issue, though activations are. Having initiative means you get to decides who activates first. Having an Activation advantage means you get to out-activate the enemy towards the end of the turn, as you possess more units than the enemy.
That said, I am less on the fence than I was before.
Phil is saying that the turn ends when the last unit has been activated, and there are no units left to activate. However, he is, also, saying that if you have not activated your paradeploy units by the time he has activated his last unit, then you have forfeited your right to do so for that turn. It is here - sorry, Phil, that I am going to shoot his argument down, as well as yours, Bryon.

Bryon, reverse the situation.
By some miracle, I have more units than my enemy, and one of them happens to be para-deploy. I lose the initiative for the turn. Here is how it would look:
- Activation One
- Enemy activates
- I activate
- Activation Two
- Enemy activates
- I activate
- Activation Three
- Enemy activates
- I activate
- Activation Four
- Enemy is out of units and cannot activate
- I activate
- Activation Four
- Enemy is out of units and cannot activate
- I activate my paradeploy units (enemy has passed twice)
I can choose, now, to land my para deploy units. Yes, I know that the difference here is that
I[/i] have not passed. I realize that this is one of the sticking points of the discussion, however, I offer it to show that if one side can hold them to the last, then the other side should be allowed. Therefore, the definition of the end of the turn should be when all units that are able to activate have done so.
By Phil's definition, my turn would have been over before I could bring in my Para Deployers.
That said, Para Deployment is, by definition, a Special Ability. As such, it is not, necessarily, subject to the "normal" rules. It is, now, even more apparent to me that the Para Deploying Unit should be allowed to be activated any time during the player's turn.
Remember, this is a
very expensive, one-time use Special Ability.
Further, I think that this discussion has reached a point that it needs official ruling.