Hi Chris, the first step I would take is to setup a ppc/adwords listing in the first spot. It shouldn't be too expensive. You'll start to gain the benefits this afternoon. If it ends up costing a lot, you can stop/pause the campaign anytime. If it doesn't provide the results you hoped then you should consider reevaluating if getting up above the competitor for this one listing is worthwhile really.
From there, optimization takes time. With your ranking at #6, what time of result is that (organic, local?)