Ask HN: Help me transition my first app from ads to SaaS

I recently released my first app for iOS and Android: budgeting for families [1]. Think YNAB, but without the $60 price tag and no need to spend hours to set things up. The launch was a success in that I am getting continuous user signups. There is a core user base that is active and growing feedback has generally been positive. I think I built something people actually love and now use multiple times every single day. Moreover, it provides a value to my users in the range of $100's per month.

The problem is, I am not making any money from it and cannot see how I will unless I change things up. Initial idea was to add an AdMob banner at the top and give the app away for free. This doesn't work because my CTR is pretty much 0.000% on most days. Some days it goes as high as 0.07% but the CPC hovers around $0.05 so it's peanuts.

I personally don't like ads, in apps I use, or in software I make. It misaligns incentives: my goal is now to make people click on ads instead of using my app. This is the reason I don't want to add interstitials. I used ads in the first place because it let me put off deciding how much to charge.

So, I'd like to transition to a subscription or purchase model. Simplest solution: charge once for an app without ads. Problem with this is that I run the backend service, and once the user signs up I will never get anything else from them. I would price it somewhere between $3-8 but I don't think many users will think it's worth it just to not see a small banner.

Second idea is to restrict usage: you can only track X budgets, or you can only share them with X users before having to subscribe. The problem with this approach is that the vast majority of the current users have 1 budget that they share with nobody or just 1 other person. Not much of a long tail here.

Which would you choose? Also, how would you handle whatever transition you'd choose for the existing users?

Thanks in advance!

[1] http://family-fortune.ridgebit.com/