DIY quadcopter very unstable flight

I have a quadcopter that I designed and built from scratch. Its quite large and holds a NEX-5N up the front and a 5S 10A battery at the back, so the weight is quite biased in the pitch rather than roll.
Here’s a picture

Im on PH copter 3.3
My hover is at about 55%
When I hover in alt hold or pos hold, it is very steady, but when I try to auto-land, it starts to oscillate back and forth in pitch at an exponential rate, until it finally just loses control.
When I fly into the wind, it seems to be a bit more stable, but when I turn it round, it starts getting wobbly. Im not sure if it’s me or the FC though.

I had a slight crash a few weeks back due to this, and have now re-built, and am still having these problems. Im a bit worried if I try doing an auto-tune that i’ll have problems and crash, so im hoping I can get some advice on how I should manipulate my PIDs to get it a bit more stable before doing auto-tune, or if there is anything else that I might be able to change.

Here are my logs:
Link to logs

Thanks in advance.

You have some puffed batteries there, be very careful. Is it rigid with the arms locked out?

Yeah, that’s my spare battery, it’s see better days.
The arms are very rigid once locked in, but when I had that crash is after I had a rather hard landing the rear right arms slightly dislodged without me noticing, then I flew off again and it totally came out and eventually caused the crash. Moral of the story is that i keep constantly checking the arms at every opportunity.