It is actually not surprising that the Apple recompressed files are bigger. They are optimized for fast load not small size. If you do not care about size over speed, defiantly do turn off the compression. Even if you do care about speed you can do better than Apple.
https://imageoptim.com/xcode.html
So yes, turn off the PNG compression. The first thing I would do is build the ipa. An ipa is actually a zip file so build the ipa, copy it to a folder on your mac, rename the file with a .zip extension and double click on it. This will expanded it. Find the app in the Payload folder and right mouse click on it and choose show package contents. You will see all the assets. Sort by size. I am guessing you have overly large images. At that size my guess is that the extra size is likely to be caused almost entirely by the PNG files.
Consider using non retina images for some. Honestly most people wont notice. iOS will gracefully use the non retina on retina. This can save a ton of space,
Also consider using jpeg files instead of PNG for some of the files if you do not need transparency. Jpeg files are less efficient but can be much smaller. Compare both. Depends on the extent to which the images are continuous tone.
By default PNG file are 32 bit. 24 bit color and 8 buit alpha/transparency. You can save a bit of size by going to 24 bit. You can also save a lot of size going to 16 bit color or below. At 8 bit PNG files use a color lookup table. Play with Photoshop and the save for we options at PNG with bit depth 8 and below.
I have all sorts of expensive compressing software but often use the $8
https://itunes.apple.com/us/app/lossless-photo-squeezer/id704083918?mt=12
Try the 8 bit PNG option and the JPEG options.
EDIT
I did some research. I had always know Fireworks did better PNG compression. I did not realize that there was an 8bit PNG with an 8 Bit alpha channel. Photoshop supports 8 bit with a 1 bit Alpha Channel. I have always told people to use 32 bit PNG if their transparency needed more than 1 bit. In the future I will let them know the 8 bit with 8 bit alpha may be the better route, They just can use Photoshop for the final save of the file. They just need to save a 32 bit and compress elsewhere.
http://calendar.perfplanet.com/2010/png-that-works/
David