Character affiliations troubles

I have been trying for a while now to obtain the "ASF" affiliation on my character,
but either I am doing something wrong, either I do not get how it works...

I was "Navy" with ASF being in second position (maxed), so I thought by killing a few
navy guys, ASF would take over the first position

Reputation of navy was decreasing but would not lower down... I was told to try to kill
some more as the affiliation seems to need to go down 3 or 4 bars before being switched.
I tried it, and I did lose Navy affiliation, but it was replaced by "Kusari Nany" ( that came from nowhere???).
To see what would happen, I killed a few Kusari police to get rid of this affiliation, and in the end it
was replaced by.... Navy (which was way down the list after this mess) *sigh*

Back to square one... (and ASF faction still remains on 2nd... and I must have killed like 2,000 CSF by now)

You guys have any trick to obtain the affiliation of your choice?
Thanks

I gave a try to your advice Your_Uncle, and this is starting to get epic!
By killing current affiliation to neutral, I came to:

Navy > Bretonia Armed Forces > Corsair (what the?) > ALG waste disposal > Farmer (that's when I knew I had to take a break! *sigh*)

Well, I think farmers alliance shows only "Alliance" in tag name... Close enough for me to ASF Unless I want to risk messing up all my factions to give another try LOL

Grrr! no comment!

Farmer maybe better than ALG - street sweepers waste disposal?