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No, using a coil with the wrong characteristics could affect the bandwidth. I suppose you'll have to attach the resistor in parallel to the coil rather than have the coil wrapped around it. Not sure what effect that will have.
Seriously though. This is a really subtle thing and I really doubt you're going to notice much of anything either way without test equipment. Try shorting on of the coils out with a jumper wire and see if you notice any difference.
None of this has anything to do with your bigger issues. The focus control should not be at one extreme and you image is off center. I would not be surprised if the two are related. Namely, the focus coil is not mounted in the correct positon.
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