11.38 volts is less than zero. A discharged battery runs around 12 volts, and a fully charged one at least 12.6 volts. It really sounds as tho the battery is not being charged.
I have a solar battery mounted on the canopy above the cockpit. It is rated at 85 watts, I think, and delivers a couple of amps which I split between my two starting batteries. The start batteries have no other load on them, and the continuous amp of charge (during daylight) keeps them topped up when I am away. I have a smaller solar battery on the hood of my truck. I remove the negative terminal to kill the load, and let the sun keep my truck battery ready. My two house batteries are kept up by a float charger on shorepower that maintains about 13.5 volts. Of course, all four batteries are charged when the engines run.
I like the solar battery. No moving parts, no reliance on dock power, just keeps the start batteries ready. Once the engines start, there is juice enough for all.
I have found that the extra expense of Optima batteries is worth it. The AGM technology is excellent for boats.
1975 32' Flybridge Sedan, twin Perkins 6-354 diesels, 1:1.53 velvetdrives, 16 X 19 props. Merritt Island, Florida