Your current roster does not sound so good!
As for the feeling against the roster I think you picked up the wrong vibes - when I said it was not good for long term health that was based on medical issues. As far as I am concerned, despite the fact that it isn't too good for you, I think it's a great roster as you get a fair bit of free time. Naturally a more stable roster which does not chop and change is better health wise.
With regards to overtime - there are very strict rules governing rest periods between duties. For example you could not do an afternoon shift then go in next morning for a morning shift - it's not legal!
As a security guard although it could be argued that you are responsible for peoples lives, it is in no way comparable to the responsibility of controlling aircraft (not being dismissive or elitist - it's a totally different type of responsibility in the way it is carried out).
If you were to take a few days off i.e. a cycle, then you could be offered overtime in those days, similarly, depending what you did with regards to days 5 and 6 of the 10 day cycle, there may be opportunities to do overtime on one of your 4 days off.
Overtime is also limited to a maximum amount per year - an agreement between the Union and Management.