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Let us know what your starting system parameters are before you start trying to tune it. I'd like to know the frequency of your sampling the current and throttle and how they are filtered (rolling average? details on that). I'd also like to know your PI loop frequency. It is a good idea as well to decide on an intended response, for example, 5% overshoot, 1 second 90% response, 1.1 seconds to 2% error.
My digital control systems text book is at home burried in the "to be sorted" pile of boxes, but I'm sure you could get some starting values by looking at digital control system theory online with using the parameters listed above.
Edit - is it also possible for you two rig up 3 push-buttons with resisters that would give you 5%, 20% and 50% throttle? These would let you datalog or scope the various responses.
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