Been fighting the same issue with mine, just yesterday. Whenever they run out of water quickly, it almost always a bad lower element.
Mine is testing with good ohms ( 15), but it's not holding the heat. Like said earlier, even though I flushed tank, I'm betting it's all covered with heavy calcium deposits. I am going to replace it and see what happens. I thought about a new tank, even though this one is probably 15-20 yrs old, but it's got a special liner in it so the innards is supposed to be guaranteed not to rust. When I pulled upper element, inner walls looked brand new.
I also made the mistake of removing the dip tube out when I replaced the conection nipples on the top. Thankfully I saved it and was able to modify it and put it back in. The cold water was coming in and mixing with hot water and then right back out into house.The cold water now comes in at bottom of the tank like it's supposed to. After watching some youtube videos, guy on there says this is actually common and many people replace the tank when the dip tube has just fallen off.