I'm impressed... great concept.
I've uninstalled JD to see how this works for me. My first impressions - apart from the vastly improved deep sleep time of course - is ease of use (JD is diabolically complicated, at least for me...).
One thing I do like from JD though, is the ability to program the sync frequency of "syncable" apps - there are about 6 options, including 1hr, 3hrs, 6hrs, 24hrs.
I found this very useful since I would let Whatsapp (contacts not messages) and Google contacts sync every 24 hours, Google calendar every 3 hours, weather every 3 hours etc.
I use Kaiten email push to receive my emails: being push, they arrive every time the data connection is restored. So that option described above really cuts down - I think - on phone activity, compared with linking the sync to the wakeup period, or letting them sync as they want to.
Could that be done in Deep Sleep Battery Saver?