TolpuddleSartre:
Isn't there a variable speed servo library?
Yes but it doesn't accept a specific time to move from A to B. Just a notional speed to move at. I suppose you could try calibrating the various speeds.
But it's probably easier to use the Sweep technique of moving in small increments (which is what VarSpeedServo does internally) and calculate the time required for each increment yourself. That's all you can do with servos because they have no actual speed control. You have to move small amounts and pause between moves. E.g. if you want to move 30 degrees in 10 seconds pause for 1/3 second after each 1 degree move.
Steve