Rear deck latch problems

I've been having ongoing problems w the rear deck latch on my 08 Prius. Initially it took extra pressure to engage the latch, then began to stick in the locked position with the door up, so I couldn't shut and latch the door. I tried lubricating the latch to no avail. With the door open idiot light on (though the door is locked) , it succeeded and requiring a replacement auxiliary battery. I finally replaced the latch and striker both and it's still a problem. Had my garage look at it, no luck. Tried stacking shims behind the striker to more fully engage the latch. Nope. I do notice when I manually operate the latch, the "door open" light doesn't go out until the latch rotates another 30 degrees or so beyond simply engaging the striker, so for whatever reason, that latch is not fully rotating (it is new). Naturally I'd like to fix it properly, but in the short term don't want to contribute to the demise of another accessory battery.

This may be related, but my electronic key with a new battery fails to lock the car (this must be done manually) and will not unlock the car with the key in my pocket (I have to press the button on the key)

Thanks for your thoughts.