From your description I assume the hotspot is necessary -- you are doing more then trying to make a voice call. For my needs I need to have email access, download a few files, work on an update, and send my work back home on the satelite. Usually 2-3 connections a day when I am away.
Over the years I have rented imersat bgan phones of various different models. You do get wifi, but it is slow -- think dial up speeds. The last one I rented was three years ago for a 14 day Galapagos trip. It was about 3 or 4 pounds, about the size and shape of a small notebook PC. You unfold the cover to the appropriate angle and twist the computer to face the approrpriate satelite. There is a geiger counter beep to help you zero in on the ideal angle. The speed is slow, think dial up at best, streamline what you load and consider getting an email account for this trip. There are also several programs designed to condense the email especially for satelite use, the rental companies can guide you to the appropriate software. I need to check in and download and upload files once a day when I travel, and the phones work pretty well for this, but as others have said they don't work particularly well for incoming calls. You need to be outside with the phone turned on, and line of sight to the satelite.
The companies have always insisted that I can't use the imersat begans on a boat without an expensive mounted antenna. I have probably rented Sat phones and used them on boats more then 10 times and I have always been able to make them work except when I was in Greenland, and the Satelite was too low on the horizon for a reliable connection. The most difficult condition besides very rough seas, is if you are on anchor and swinging in a big arc--- although with a compass and steady hand you can slowly twist the unit and maintain connection. My connections are relatively short 3-10 minutes, and sometimes it has taken several tries. I don't know how much you are downloading, and I will admit that it is usually stressful trying to get and maintain the connection, but for my needs and use it has always worked. I have routinely ignore the advice from the companies that rent that I won't be able to get a connection on a boat, but your mileage may be differ. The size of your downloads and uploads may also rule this out as a possibility.
Having given the long winded explanation, and even though I have direct experience making it work, if it were me I would take the advice of a prior post and investigate what the boats offer that have a Sat connection before risking a bgan rental.