Anchorages can be a challenge on the Gulf Coast. We are there now too.
Do you have Claiborne Young''s cruising guide for that area? He gives very good anchorage information, and we always check it out ahead of time to pick an candidate anchorage or two before we set out. Our draft is about 5.5 feet, so depth is always an issue and a challenge.
Re: pulling up the anchor. After many years of cruising, I have come to the conclusion that an anchor windlass is a MUST from a safety angle. I''ve seen so many people with strained backs from hauling up anchors...and in an emergency, with the adrenaline pumping, it is very easy to do serious physical damage that could adversely impact the cruise.
Seems to me that a hand-operated windlass would work fine for you guys. The farther afield one goes, and the more and potentially deeper anchorages that may be encountere, the more an all-chain rode is needed, and, I believe, the windlass should be electric with a good manual backup in case the batteries go down.
Hope this helps!