In short:
? Is there any way (other than a wardec) for a member of the militia to counter-attack another member of the militia who attacks his own militia, WITHOUT taking standings hits with that militia when you counter-attack? And if so, what are those specific circumstances?

No.

Its been like this forever, you will always take a factional hit if you shoot at another militia member regardless of what they do.

Step 1. Get two alts with +10 Faction Standings into 3 man corp.
Step 2. Have third guy AWOX friendly militia, standings eventually go to -10.

(10 + 10 - 10 )/3 = 3.33. Your corp gets to stay in Militia.

Step 3. Go to Step 2.

Pretty much this and the similar ghetto version:

1. Get alt with 0.0 standing and corp management skil.
2. Create corp and join militia.
3. Awoxer joins corp.
4. When corp gets warning about standing (is it still 7 days?) awoxer leaves corp.
5. When corp back in good standing, awoxer joins for another week.

Pr0 version would be to have 2 alts and 2 alt corps so you can alternate week on / week off.

Running into a possibly pretty bad issue in Faction Warfare. Stuck at work, so I can't test it. Can someone verify?

The Situation: A guy in your FW Militia shoots a non-outlaw member of the same militia. At some point in there, the Awoxer is set suspect, which should let anyone shoot him.

... EXCEPT, if you're sitting right there, and in the militia, you still can't shoot that awoxer because you'll take a big hit to your standings with the Militia?

For this test, we need:

* The Test server, so everyone doesn't get their standings shot to hell on the live server.
* 2 non-outlaw members in the same militia, who aren't in the same corp.
* A third militia member who can be outlaw or not, and not in the same corp as the guy who will be our awoxer.
* (Optional) A non-militia neutral party, to observe and confirm flags.

1. First non-outlaw militia member shoots 2nd non-outlaw militia member.

? Can the aggressed militia member return fire WITHOUT taking Militia standings hits? Yes, I get that he's at the very least in a limited engagement and won't take sec hits, but does that affect the Militia standings issue?
? Can the third militia member join in on the now-suspect-flagged militia member awoxer without taking Militia standings hits? (He won't take sec hits, but what about Militia?) What if he's in fleet with the aggressed pilot?

2. Have one non-outlaw guy pod one of the other guys. Then have the guy who now has kill-rights come back and activate them.

? Can the militia guys sitting there next to that kill-right-activated guy attack him WITHOUT taking militia standings hits?
? Do even kill-rights fail to make it possible to counter-attack a militia AWOXer without taking militia Standings hits?

? During all this, what flag change is the neutral party seeing?

In short:
? Is there any way (other than a wardec) for a member of the militia to counter-attack another member of the militia who attacks his own militia, WITHOUT taking standings hits with that militia when you counter-attack? And if so, what are those specific circumstances?

I don't think it's as simple as "if you can attack them without taking sec status hits, you're okay", because if that was true, people could shoot -5 outlaw militia members all day without the Militia caring, and I don't think that's the case.

Or maybe you could just ask the aowxing alts of your own militia in Caldari and Amarr... oh God not another hyprocite thread.