How are you adding the timer? Arena doesn't usually have one, so... there might be some kind of inherent conflict. I also have the HUD overlap if I try to put a timer in with arena mode so I'm a little confused what you have going on.
I poked around at the entities ingame and it does seem to just be an inherent conflict with arena mode. For whatever reason adding time simply does not work, neither on the built-in timer nor custom ones... as you know.
However, the SetTime input does work, so I'd suggest using that as a workaround. Set up a math_counter that starts at the same number of seconds as your timer, and sync it with a logic_timer to decrement it 1 each second. When you want to add time, add the value to the math_counter and send it a GetValue and have OnGetValue pass on the new time to the timer via SetTime.
I'm... not even sure what you are doing there. Way more entities than I expected. I don't think there is any need to have more than one counter, that is just complicating the issue.
However, there is one key issue. You are assigning a value to the "parameter" for SetTime. Don't do this, it defeats the entire function of the counter. When a OutValue or OnGetValue is fired, the current value of the counter is passed along as the input paramater if it is left blank. So it is getting set to 60 seconds, because you are setting it to 60 seconds.