FYI - Taxis have been approved for 24 hours per day (except for 7am to 10am). There is a taxi rank you can just turn up at too! I am not sure about taxis coming into Ma Wan/Park Island, but I think you can get a taxi TO the island any time 24/7 and that it is only picking up passengers which cannot be done from 7am to 10am.
Originally taxis (maybe taxi pick-ups only) were allowed for a smaller part of the day and it was increased last year to 21 hours per day. So, we are actually expecting taxis to go totally 24 hours in the not so distant future, as the taxi service so far has been a success and has not impeded on the traffic-free 'green' lifestyle on the island. The taxi rank is right next to the toll booths where you come in from the Tsing Ma bridge so the impact is minimal to none at all.
I can confirm there is no planned car park (which could also easily be build out of the way of residents), but I did read that a government source has said this will happen when the Tuen Mun - Airport tunnel has been completed as the Tsing Ma bridge will see a considerable reduction in traffic, enabling it to cope with additional traffic from Ma Wan. As to the reliability of this source, your guess is as good as mine!!
Reading these old posts which so strongly say taxis will not happen, make me think that anything is possible! The latest elected district councillor for Park Island actually pledged to consult and urge the MTR corporation to run a feasibility study into a possible Park Island/Ma Wan MTR station. It would be an impressive bit of engineering to build, but this is totally possible as we have the Tung Chung MTR line passing right over us inside the Tsing Ma bridge so we're not talking about laying additional train lines, tunnelling or bridge building! The possibility of this is very exciting, and although it is probably not so likely, there is a new tourist attraction set to be built on the island (where the old fishing village is currently located) so with an increase in visitors to whatever the attraction is, an MTR station could be a reality.