This app was mentioned in 5 comments, with an average of 2.60 upvotes
Have you already tried an Android call history app, that gives specifics, to see if it offers more info, like:
https://play.google.com/store/apps/details?id=com.pa.calllog.tracker
or
https://play.google.com/store/apps/details?id=com.teral_soft.calllog
I don't know of any Fi-specific methods (waiting for my 5X). I've never used it, but it looks like there are a few apps that can export your call history to a spreadsheet. Here's one: https://play.google.com/store/apps/details?id=com.pa.calllog.tracker
Not sure whether it'll help, I use an App Call History Manager to look at and export my call history from my Z3C. (useful for reconciling against my bill). I've never had it not store a number yet but, there again, I've never had to resort to your work-arounds to make or hang up from calls either!
Might be worth a go?
The default call log in the phone app can't be searched. If you try something third party like this maybe, but be warned, I have no idea how safe/sketchy those apps are.
You should also be aware that the default call log for Android only holds 500 entries before it starts overwriting old calls, so hopefully it wasn't too long ago, or else you're going to have to request your phone records from your carrier.