Very nice HR trailer you got there Jason. I am no help on how to get to the water tank. As for the battery, I would take some measurements (LxWxH). That will give you the max size you can fit in there then go to the store and find the size that will fit. BTW, I would get a deep cycle battery as opposed to a starting battery. Also, if you have the room, I would get 2 6 volt batteries as opposed to 1 or 2 12 volt batteries if you plan on doing a lot of dry camping. I put 2 12 volts in our MH, but my wife's idea of dry camping is not hooking up the water hose at the RV site LOL. So off grid camping is not something I have to lan for. If we do do any it for a few hours, maybe overnight, and those 12 volt batteries have enough storage for that.

I have a 84 32' Imperial that looks exactly like yours on the outside but my interior looks a lot different. The only leak you would have in that area is from the sink not the tanks. The tanks are under the floor and there should be a large access panel 4'x8' on the bottom by the axles for that kind of problem. If there are no water leaks in the sink area I would check for leaks around the door or ceiling. The switch by the door when turned on will light up the light under Panel above the door. There is a switch inside the door frame that will light it only when you open the door. Smaller Car Battery will work fine, 2 if you want. Measure the height before buying. A new one will be fine for several years not having to start a car and the converter will keep it charged. When not using the trailer I would recommend taking it out and storing it. I'm also a member of Vintage Holiday Ramblers where you can also get a lot of info.

With the holding tank issue,,,, think in terms of the assembly process and what the manufacturer would do if they had to replace the tank in the future, They have an access panel on the under side just for that purpose, An RV tech, wouldnt  rip apart an interior area to repair a holding tank,, whether it be a black,grey, or fresh water tank.They make them accessable from underneath, so the integrity of the flooring isnt comprimised by cutting through it. I would remove the panel and add water slowly to see if the tank is cracked or if its just a fitting or loose connection, Do a process of elimination.In the past, I have addressed issues with a holding tank and 99% of the time it was a connection that vibrated loose. The other 1% was a cracked tank, from being full in a cold winter and  freezing..  As with using a car battery,, your dry camp usage is limited because a car battery is a short cycle use and drains faster then a marine type deep cell battery, Twin 6 volt deep cycle are preferred as the best route.