If you plan on doing the shaft log conversion which I’d recommend because it will be a once and forever fix, you can get the boat water ready for the remainder of your season in a day or two. (Depending on drying time of whatever caulk you are using.) it will be a temporary fix but will allow for boat usage till the end of the season.
Open the HDS lid, let everything dry out thoroughly, caulk all the way around the inside bottom of the HDS box and put the lid back on using marine silicone.
*edit*
Don’t use silicone inside the box. It will screw up any later repair.