You can try telling AXA that you've found the exact same TV still for sale as I believe they are required to replace it with the same TV if possible. but if the same model is not available anywhere then it does just need to be a matching spec TV.
If they persist in saying they want to pay out with the LG then go through the specs carefully and compare them with the JVC, if the LG is significantly below the specs of the JVC in any way then you have a reason to refuse it, if it matches or exceeds all the specs you've not really got a leg to stand on.