Edit - I checked out your app and saw that you had to disable some features. If I were in your shoes, I would pull a Whatsapp and monetize immediately. As it stands, you don't have any power and major power imbalances tend not to work out in the founder's favour.
Have you considered charging a dollar annually (like WhatsApp previously did) and seeing if current users will pay? If you’re out of funds, and have no seed round lined up, why not attempt to monetize immediately?
Also, have you explored if Amazon has any accelerator programs you’d qualify for to get some AWS credits to tide you over (paging jeffbarr).
$1 per year might not completely solve your cash flow problems, but it will bring some money in and give you some powerful evidence to help with your fundraising.
How can you save money on hosting?