I'd also like to back-up @Kumar Paj in that you need to get some paperwork done and be ready to go, which is what I did with the mortgage broker to get started on my first deal.

With a local shop, my main concern would be if they are up with current technology to facilitate doing it online or if they need a lot of paperwork signed in person, etc.

Start the paperwork now, but give them a chance to go peacefully. 

You are essentially doing a self- redemption. 

What we found is that you can get the documentation at no cost and with no proof of need, but our lawyer said as a landlord in Florida you're not obligated to accept the paperwork unless it's backed up by a doctor's letter.

The LLC formation process involves completing paperwork and filing with the secretary of state, paying a formation fee, and creating an operating agreement.

Ok cool, now you need to pay your attorney 10k to draft the legal paperwork for the syndication.

Ideally, finagling not even having to put any cash down by refinancing and taking that bit of cash to use as the down payment for the construction loan, it would be great to have our current lender managing all of this so they are essentially releasing the lot to themselves again for the construction loan. 

Essentially, the questions is - does anyone have a recommendation for a specialist in self-storage who can assist with this project from infancy to completion (including securing bids, consulting, management, etc.)?

@Robert Leonard is exactly right..standard VA home loans are intended to put military members and veterans into move-in ready homes that don't require significant repairs.There is a separate loan product called the VA Renovation loan, which essentially packages a home purchase loan and a home improvement loan into a single product.