"Is there anyway of finding out which outstanding secondary schools still have places for Sept 2016?"
If a school currently has a vacancy and no waiting list, then they must give it to the next person who applies, irrespective of where they live. So you can apply from your current address (but your DC will need to take up the place in a timely fashion, usually a couple of weeks). So perhaps you need to list all schools you see as possibles, then ring to ask. If it's a year 7 starter place, then you are not getting a straight answer because the shake down of waiting lists following this year's offers will still be going on, and a place they say they have today may not be there in a few days time. For other year groups it might not be as changeable.
'Or what chances do you think I have of getting a place under appeal if new to the area in a small area with two outstanding secondary's both oversubscribed and the next nearest school is over three miles away?"
Next to non-existent, I'm afraid. Schools are not permitted to hold places back just in case there are new arrivals to the area. And secondary age pupils will be expected to be able to travel independently (transport costs will be paid if over 3 miles, indeed transport might be provided depending on what the public transport is like).
As it sounds like you would be making an in-year application, then if the school is full the chances of appealing successfully on grounds of error seem remote. You would have to make a case on the 'balance of prejudice' ie show the detriment to your DC by not attending this school is greater than the detriment to the pupils already there from being in a bigger class. That does mean that you need to know a lot about the school and what it uniquely offers that benefits your DC so much.