Welcome to T-Net, Leeland. There is a lot of great info on this site and very knowledgeable members.
The treasure salvage community here in Florida is tight knit and everyone pretty much knows what everyone else is doing. They are not interested in "exposure" as you put it, unless it is to attract investors. The operating expenses are enormous and everybody is looking for funding. My advice to you would be to contact one of the lease subcontractors and see if they would be interested in allowing you to film their operation for a fee. No guarantees, but in this business, like everything else, money talks.
Generally speaking, the treasure diving season here is from June to September, mainly due to sea conditions and visibility. Good weather might extend that for a month at either end. Now is a good time to make contacts. Most of the major players post on this forum. Good luck.