2 strikes and you're out. This is the same all the way through ATC training and even in the field. They do this because it doesn't give you time to prepare. ATC is about being confronted by a problem, and coming up with a suitable solution (but not necessarily the best) 1st time.
You could try Airways, but beware, their recruitment process is almost identical. Yes you will have to go to New Zealand for the testing as it is done in the classroom. If you pass that they will fly you at their expense to Christchurch for the Assessment centre and interview.
While they won't be able to specifically tell you that you've not been accepted due to your age, it may well be the case. Having ATC trainees your age makes them very nervous. It's not about how many years of service they will get from you. It is about the ability of people to 'learn new tricks' as they get older.