I know planning a DW can be overwhelming especially with the issues you mentioned. We are of a similar mentality to you about wanting a private experience (absolutely do not want a bunch of on-lookers in Speedos) and feeling guilty about the costs associated with a wedding. I believe it can be done!
One of the ways we are trying to manage this is that we are looking into smaller, non-touristy areas for the ceremony, reception, and stay such as Tulum in the Mayan Riviera. This way, there's not as much traffic on the beach so it will feel more intimate. There are a few AI hotels in the area, but many others are small hotels and some are boutique. Another reason we are highly considering this area is because there is a range of hotels that can meet a variety of budgets (ie, $75.00 per night to $250.00).
Again, I know it's overwhelming, but I am confident that if a DW is what you want, you will be able to pull it off in a way that feels right for you and your FI.