Okay, so I was incredibly excited when I saw this post because I have a small scanner that I paid about £100 for because I wanted to scan in all my negatives before I came to Hong Kong. I scanned in most but brought the rest with me to scan here. However, I have searched and searched for my scanner and can't find it and have been wanting to check some of my negatives.
So I thought I would give your process a go. Firstly, the problem with scanning it on another phone (I used an iPad) is that it causes all those squares. Also, I felt like I couldn't get close enough so I added my olloclip x 10 macro lens and voila it was a lot better - the squares were smaller. If the negative is a slight distance from the screen then you eliminate the squares. I have negative holders from my scanner and think I will try that next. However, a better solution might be to set up a light table with a piece of glass and a lamp underneath.
I downloaded your picture and although I can improve the contrast and lighting using Snapseed, the squares remain. I tried simplifying it in iColorama and using edges to bring back definition but it gives it a more painterly look and it no longer looks like a photograph.
My set-up:
1) I created a 'white' photograph by going into iColorama and choosing a blank template which I saved.
2) I then brought this up on my iPad and put the negative on it. I then got my guerilla pod and placed the iphone directly above. I don't have a spirit level so I had to guess whether it was straight. A spirit level would improve overall sharpness I have no doubt. I used the app Camera+ with the high resolution TIFF option so that I would get a high quality picture and this definitely made a difference compared with some of my quick native app attempts. As Mat mentioned, I inverted the colours on the iPad (sorry, correction iPhone) by going to General>Accessibility. This means that you see the proper picture through your camera.
3) The pictures are however taken as a negative so I took them into Photoshop Touch and inverted them using the adjustments controls.
Below is my set up. You can just see the negative at the bottom of the ipad screen. The actual picture you see on the iphone is what the camera is seeing on the negative (one of the boat).
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Here are some of my examples with the macro lens. There is some blurring at the edges which is probably caused by the fact that the negative is not flat and may also be the macro lens. If you look carefully you can see little squares on the boat pictures because the negative was concave up on the screen. When it was concave down (edges touching but not middle), there are no squares:
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I improved the photos slightly in Snapseed using Tune-Up but see that I could have put up the warmth as they are looking awfully blue and a little light! Also some of the negatives needed a good dusting. The pictures were about 8Mbytes each but I have reduced them to only about 100kbytes for posting purposes. I can put up higher quality if anybody is interested.
The original picture was taken with an ordinary instamatic camera in the middle 80s.
Just out of interest this is one of the pictures I scanned in using my scanner (which admittedly is not high end) and I think that the iphone version is sharper when I compare them side by side which was a big surprise.
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I haven't changed much - just become a wrinkly with more bags and sags. 