Interesting..
Your system is interesting but quite inefficient. I would suggest that you invest in a true battery monitor like the Xantrex Link Lite or the
Victron BVM-600 (LINK).
The TV:
You mention that you purchased a Toshiba 19" line voltage TV. The max rated amp draw for this device is .8 amps at 120 volts. When you use this device on a 12V system, through a 100% efficient power inverter, of which there is no such thing, the best possible current draw in amps you would see at 12V is 9.6A just from the TV! Unfortunately you would need to add inverter inefficiencies to this number which would raise your 9.6 amp draw at 10% to 10.56A. At 20% it's 11.52A. That is a LOT of juice and we have not yet added the stereo!!
By choosing a dedicated 12V LCD TV you could have saved a significant amount of current draw on your house bank. We also run a 19" high def TV only with built in DVD that only draws 3.9 amps with the DVD player running. If I run this same exact TV through a 400 watt inverter it draws 5.2 amps, same TV, just running on 12V vs. 120 volts. 3.9 amps at 12V to 5.2 amps via a 400w inverter is a full 25% more current use.
When I run the same TV through my 1200 watt inverter even more inefficiencies are added. Running off the 1200 watt inverter leads to a current draw of 5.8 amps. 3.9 amps at 12V to 5.8 amps via a 1200w inverter is a full 32.8% more current use than running the same exact TV on direct 12V. In short it pays to buy a TV that will run on 12V as opposed to only 120V.
The Stereo:
Your Samsung stereo is rated at a max power output of 1000 watts. 1000 watts at 120v is only 8.33 amps but when you run this same stereo on a 12V system the potential current draw at full rated power output, which will likely never happen for very long, is and could be 83.33A. Of course your stereo is lying to you about its input and the output is not what the input is so you are likely in the 6A to 18A range when run inverted.
You also said:
"A previous owner had converted over to a two battery system"(a cranking battery and a house battery)"
Let's assume that you have a two battery system consisting of two group 27 batteries, one house & one start. It is common knowledge that batteries should not be discharged below 50% if you want to maintain a good cycle life and attain longevity.
The average group 27 battery is about 100 amp-hours in capacity. This leaves you with only 50 usable amp hours when you leave the dock at a 100% state of charge. Of course if you anchor out overnight and charge off the alternator you really only ever re-charge to about 80-85% of the banks rated capacity. This unfortunately leaves you with only 30 usable amp hours.
At 50 usable amp hours on your single battery house bank consuming nearly 10-20A for entertainment, which does not include any other devices like depth, speed, wind or VHF, you have 2.5 hours of TV/Stereo use before you have depleted your bank to the 50% level.
As I mentioned above it is a wise idea, especially with your system, to add a battery monitor so you know exactly what's going on. The gauge on the 1200w inverter should not be trusted and they are there mostly for looks not accuracy. While it is possible that you are only burning 8.3A, which would mean the manufacturers specs are fairly bogus, this is still a LOT of current to burn up on just a TV and stereo with a single battery bank..
This entire system could have been done very well, and actually had higher sound quality (HTIB's are the bottom of the pack when it comes to accurate sound reproduction), with a 12v DVD car stereo that has a virtual surround feature, similar to a Bose 3.2.1 system, and a 12V TV. A dedicated 12v system consumes considerably less current. At a decent listening level our TV/DVD/Stereo consumes a grand total of only 5.1A.. When listening to music only our car stereo with four 4 ohm speakers consumes 1.6 - 2A at 103db which is VERY loud.. We rarely play the stereo at 103db levels as the entire bay would hear it..
One can only go by the specs provided by both Toshiba and Samsung to be correct in their specifications but a battery monitor would tell you precisely what is going on. At the very least you drastically need to upsize your battery bank based on the system you are using..
Hope this helps.