Turn the kitchen sink on for hot water. You said it won't get hot.
While it's running, go to the heater and feel if the hot outlet pipe is getting hot and cold is cold.
Open bathroom faucet that you said makes the kitchen water hot.
Leave them running if the kitchen water now gets hot.
Go back to the tank and feel if the hot outlet pipe is getting hot and cold is cold.
Rereading the thread, it does seem as though there is a cross of hot & cold as John was suggesting with the recirc line.
Diagnostics are difficult over the internet, but I'm wondering if the dip tube on the previous tank was swapped to the other inlet/outlet and now the newer tank has a dip tube on the hot piping and the cold fills the top of the tank. It's been years and I've only seen it once where this was the case, so I can't quite remember the symptoms. Try the test anyways, maybe it will ring a bell with me or another member.