Thank you so much for your advice on /r/bandmembers and /r/WeAreTheMusicMakers. We'll post it on Reddit tomorrow; today we focused on HN :). I'm not a regular Reddit user myself, so I truly appreciate pointers to relevant subreddits.
Regarding your use case: Unfortunately, we don't yet have support for importing recordings, but I think it's safe to give it a try on a regular practice session. You can export from Tape It the same way that you export from Voice Memos, so your existing workflow will work just fine. To export, open the detail view (either by tapping on the mini player or by long-pressing a tape in the list), then tap the three dots in the top-right corner and choose Share from the menu.
We've also been using the app ourselves for our own music making during the entire development, and we have absolutely zero tolerance for crashes or data loss. Even in cases like a sudden termination of the app, say because of your device overheating or battery issues, Tape It will recover your partial recording on the next launch.
Currently, Tape It only supports markers for individual points in a recording, not for marking a time range. You can add a marker during the rehearsal as well as add or edit them afterwards. While you record, Tape It keeps the screen on and prevents the phone from being locked, so that adding a marker is always just a single tap away. We were originally worried about the always-on screen draining your battery, but to our pleasant surprise those worries were really unnecessary.
One of the features on our todo list is some kind of text-marker that allows you to select interesting regions in your recording. Our current thinking is that once you start selecting regions in a text, the regions will show up in the list instead of the whole tape (although probably grouped by tape - it's a bit unclear yet). There won't be any destructive editing, though, so you can never cut and accidentally delete a part of a recording. Once we have that, we hope that you don't have to do the manual extraction anymore.
Regarding labelling a song: try recording speech and recording music. You'll notice that non-music regions are rendered in grey in the waveform. That way, you can easily spot the gaps between the different pieces you practiced.
I'd also be curious about your use of Dropbox: who do you share these recordings with? I'm asking because sharing (within a closed circle) is really high on our priority list, and we'd love to learn more about every use case :).
Please also feel free to also email me directly at thomas@tape.it for a continued discussion :). I'll continue to check this thread, too, but in the long run email might be easier.
And again, thanks for your reddit suggestions!