[Everpix founder here] Interesting idea and no we didn't try negotiating with Amazon. Not sure how much room there is here?
However it's important to keep in mind in a situation like this, and at this scale of burn rate, you're not looking for a solution to shave off a few thousands $ left and right, which is kicking the can down the road (if even), but for a long term solution.
The key problem here is that I don't think you can realistically switch a business built on the VC funding track to the bootstrap track without the collateral damage of killing your company's essence i.e. the product.
For instance: when suggesting to have fewer employees, that is implying you have room for that or that your employees are interchangeable, which is far from the truth. It's not like we had 5 tech support people, and we could have downscaled to 3. We had hired quite slowly and were already as lean as it gets i.e. 1 person per project: iOS, Web, Infrastructure, Science, Design, Imaging / QA. All these folks were working at full capacity managing a multi-platform service managing hundreds of millions of full-res photos with ~100 servers, displaying photo collections of 10,000+ photos in very responsive apps, and running cutting edge computer vision science at a scale no other consumer photo startup was doing (the closest was the semantic search in Google+ Photos). You can certainly cut salaries (which we did and only works up to a certain point in the very competitive SV hiring market), but you can't remove positions which would be akin to extending a bridge to nowhere.
Regarding the infrastructure expense, I shared some thoughts here: https://news.ycombinator.com/item?id=7041640