If you want to stay with a combo type setup like you have now you will find that TV/Blu-ray (built in) combos are difficult if not impossible to find. Even TV/Reg DVD combos are getting hard to find now. You can go with separates although 12v DC Blu-ray players are also hard to find but not impossible. If you current TV supports 1080p it would probably be sufficient for Blu-ray given the size of the TV. If you only watch while on shore power of course you have many options. You could also use your inverter as I assume they use little power (but I am somewhat new to the whole inverter world). If you are interested in finding a 12v DC blu ray player I can try to help you out.
Dennis