You would need about a 2% gain ($131.27) for this trade to break even by June 4th. See 2% column, Forward PnL row. 2nd graph. So, if you realize a gain of more than 2%, you would have to hedge with an equivalent number of deltas(short) to lock those gains. Note: These are forward deltas. You would have to model it daily or track the deltas from your risk viewer and apply/adjust the hedge at discrete intervals if you use the stock. Using an option creates a more dynamic hedge that re-adjusts itself exposure-wise with any movement in the underlying. The dynamic aspect of the hedge would require an equivalent option of same expiration and same delta/gamma levels. Again, a dynamic hedge means that the greeks are "matched" throughout the holding period and any existing profit is locked. Which takes me back to the idea that you should really be selling a call (spread)...LoL! You made me put on the dunce hat tonight. You better not have a 1 lot holding!
Hang on to your horses buddy, don't count your chickens before they hatch. AAPL had one good day in a week and you want to "lock in gains" - my guess very meager gains if any. With a restriction like a 30 day holding period and option debit spreads you don't have much choice but to ride them out until expiry.
You won't be able to hedge pitchout position without any basis risk. Your firms policies are designed to prevent what you are doing. In the future trade stock to start and close out with synthetic forwards.
If you buy the equivalent put vertical you will be perfectly hedged, with all your profit/loss locked in. For example if you have the 135/145 call spread, you would buy the 145/135 put spread with the same expiration. You will then have a "box". Your only risk if you leave this on to expiration, would be pin risk. This would occur if the stock, on expiration day closed around 135 or 145, (where your short options are). You would have a risk of assignment.