It seems to me you're trying to fix one problem by creating another. If the well isn't putting out sufficient volume, adding precharge pressure to the tank won't help; it may even make matters worse.
First, back up and make sure the tank precharge is correct. Determine what pressure the pump cuts on at. Then completely drain the tank and check the precharge pressure. The precharge should be 2 psi LESS than the cut-on pressure. If the precharge is higher, then the tank will run dry before the pump cuts on, with resultant loss of water pressure for an instant. Of course, you can't really trust your pressure gages; since you're probably using different gages to check water pressure and precharge it's possible for them to be off from each other by 2 psi. If in doubt, less precharge is better than more. You can have zero precharge and the system will work, but if your precharge is greater than the cut-on pressure it will drive you nuts.
Once you've got the precharge back where it should be you can investigate your original problem. As I understand it, it's taking too long for the pump to build up enough pressure to cut off. Assuming the cut-on and cut-off pressures are set to reasonable levels (say 40/60), if your pump takes two minutes to cycle I'd say you need a visit by a well driller; you're not going to be able to fix the problem yourself.