Having read through all this .... chat, I must say that appears that there are two sides discussing two things.
One asks "What ID is more suitable to my RP, corsair or pirate or a.n.other"
The other is saying "In order to have 'X' ID you must behave like 'X' faction".
The link between the two is that in order to have equipment from any faction under the current Disco rules, you need to have either A.faction permission or B.SRP.
If, as has been suggested, equipment is not the issue, then possibly pirate ID is better for you as it enables the group to operate outside the 'Laws of Sirius' and allows you to forge your own identity (or ID, as it were) and group RP.
From what you've said, it appears that the Corsair ID lends itself to you as it offers all the positioning you need. The problem is that it comes attached to a lot of cobblers that you don't like.
Being called cannibals by ignorant non corsairs for example.
The real question is why wouldn't the pirate ID work?
How about Freelancer?
What is it that stops you from using these ID's?