I know this is likely an exceedingly remote option, but should mention it just in case it could work for someone...
If you're willing to switch to an Android phone, you can ditch Dexcom's app altogether and use the hacker community open-source app xdrip (or its variation xdrip+).
The various alarms and notifications are much, much more configurable, allowing for everything you all would like, and a lot more (like, for example, custom ringtones for each alarm type).
Not to mention a ton of other incredible features not available in Dexcom's app, direct reading collection from an Android Wear smartwatch (no phone needs to be present), and a very responsive development group.
If you're smartphone agnostic, I'd highly recommend the switch. The downside is, of course, there's no warranty, guarantees, if a bug gives you totally inaccurate readings you're own your own, etc. etc. etc.