Disable notification center on lock screen (or prevent it from clearing notifications)
Naturally, I ended up solving this shortly after I posted the question. This article ended up solving it for me.

In summary:


Open Settings
Go to Touch ID &amp; Passcode
(Enter passcode)
Scroll down to "Allow Access When Locked"
Disable both "Today" and "Notifications View"


Now there is no swiping down from the top at all on the lock screen (but still available if unlocked). Thank goodness!