How to fix (2013 update)
I've tried the bugged saved game file I initially posted in my question with the current latest versions of the official patch, Unofficial Skyrim Patch (USKP) and Skyrim Script Extender (SKSE), and the saved game is now Aspect of Peryite-free.
I've configured SKSE to use its ClearInvalidRegistrations
console command on every saved game load, which removes invalid scripts left running by uninstalled mods. This feature was introduced in v1.6.7 of SKSE:
add console command ClearInvalidRegistrations
to remove invalid
OnUpdate() registrations
This prevents orphaned OnUpdate() events and
the resulting bloated/broken saves when removing certain mods. When
applied to an already bloated save, it will stop growing further and
instead shrink over time as the game processes all queued events. This
may take hours depending on the amount of bloat.
To execute automatically after each reload, add this to \Data\SKSE\skse.ini
:
[General]
ClearInvalidRegistrations=1
According* to a developer of the Unofficial Skyrim Patch (USKP), the underlying cause is because DA13 ('The Only Cure' quest) is never stopped.
A possible fix* for this:
In the meantime, load an affected save, then type stopquest DA13
into the console. That ought to put an end to that. Plus it’ll free up some unnecessarily leftover alias memory.
BTW, don’t use the console command on a save not bothered by it. Even though it may appear benign, console commands can have negative consequences you don’t know about.
If this doesn't work or if you experience issues like: NPCs not responding properly to conversation (not reply to you when you choose a certain conversation path - leaving you stuck), merchants not opening the buy/sell window, horses that can't be ridden, and other interaction issues, then the save game is most likely corrupted. Try the SKSE ClearInvalidRegistrations
console command fix I've posted above, instead.
To prevent this from happening in the PC, get the latest version of the Unofficial Skyrim Patch. This has been fixed since version 1.1 of the USKP:
"The Only Cure" (DA13) was never stopped which would lead to the Aspect of Peryite randomly initiating conversation and being unable to exit.
* This info is from the old USKP bug tracker page at 16bugs.com, which is now not viewable. The new USKP bug tracker report page of this bug is at afkmods.iguanadons.net.
Im Not 100% This Will Help But...
According To The Wiki You Need
Must have at least one Glenmoril Witch Head in inventory.
Must complete at least 1 Radiant Quest from Farkas or Vilkas, after
completing Glory of the Dead and having Glenmoril Witch Heads in
inventory.
If That Doesn't Help The Wiki (Link Below) Will Have A Bug List It Will Help Find Out What You Need To Do To Fix It
Source: http://elderscrolls.wikia.com/wiki/Purity_%28Quest%29
EDIT: It May Be This Bug
There appears to be a bug when you accept Vilkas's Purity quest before Farkas. The quest status will switch to the Completed even though you haven't completed it. Also Vilkas will not follow you to Ysgramor's Tomb. To resolve this, accept and finish Farkas's Purity quest first and be sure that the quest giver is following you the whole way through.
Source: Same As Above
Best Answer
Giving yourself items should never break the game (unless you give yourself quest items, but they are useless, so why would you?). Advancing quests with the console can be problematic (and, in the case of some quests, impossible) both because there are undocumented stages to most quests that can make important changes, and because things other than quest stages may be involved in the quest, such as opening passages, killing characters or acquiring items.
Overall I would recommend making a new character and playing the storylines you haven't played with your last character, then deciding whether you want to risk messing up your save or if you want to replay the old storylines again.