1:1:
If I switch it on with all servos plugged in (even if they are at their home positions already), the supply will say it's providing 2.7V at 5A (or whatever I limit the current to on the supply) and the servos wont operate.
Furthermore, once it is in an operational state I can concurrently send all servos from min pos to max pos at full speed and the supply will not current limit until about 4A - i.e. at 5 I see no limiting - however, with the supply set at 5A on turn on, it'll poop its pants as discussed :
It is, as suggested, directly related to the power consumption of the servos - and I should say that I have 4 different types of servos, and indeed some are more powerful than others so 5 is the average amount I have to disconnect. (I just didn't want to bog down the discussion with too much detail)
Regardless of figuring out which one is to blame and whatnot and especially considering that the system works once it's plugged and is under 'stress' am I being unreasonable in expecting this not be happen anyway?
And I guess, more to the point >> what is a workaround that doesn't involve:
~ experimenting with a higher rated power $upply
~ fiddling with little plugs all the time as I am currently doing 
Is it as simple as having a large cap always connected across the supply?