I would punt Apex asap. The guy knows the deal and he's looking to line his own pockets with a couple of grand he didn't earn.
A few ways you can go here, some dependent on what the adjuster ultimately will require to pony up the extra $2K. If he requires documentation that you actually spent the $11,500.00, then you'll either have to get a contractor, show him the estimate and ask him if he'll do it for that. Fork over the deductible, let him present the paperwork to the insurance company to collect his dough and call it a day.
Or, if you want to pocket some or all of the $2K, you'll have to get the contractor bidding the lower price to present false paperwork to the insurance company so you can collect your dough. Do not recommend.
What I would recommend is to tell the adjuster a $5,900.00 deductible will eat your lunch right now and you're looking at playing contractor yourself and subbing much of the work out for the best price. When the work is complete, you'll call him to come out and inspect and see the finished operation....and collect your dough.
Or Option C would be to give the adjuster and your contractor blow jobs in exchange for better deals.