As someone that has worked around and driven lift trucks for many years, I personally would not get up in one of those maintenance cage attachments unless I had a high level of confidence in the lift truck operator (I have encountered very few operators that would instill that level of confidence in me). I see those devices as useful in very small operations that rarely have a need to use them.
Since you stated you have two cages and have recently replaced both, I'm thinking that your more frequent needs would be better met by getting a piece of equipment designed specifically for your tasks (a scissors lift or some type of aerial boom lift). Not only are these types of equipment safer, they are also a more efficient (get the task done with less labor) means of executing maintenance tasks.
As to your specific question about reach trucks, a reach truck is more stable with the load retracted (and conversely less stable when the load is extended). That is why you should always have the load retracted when the truck is in motion. "Safe" is a relative term, and while it may be considered "safe" to extend the reach when handling non-human loads (the purpose of the reach truck); a human load tends to change the context for defining "safe". In this new context, playing it safe would suggest not using the reach functionality of a reach truck when using maintenance cage attachments.