I think your chances of getting through a special char request will improve tremendously if you choose a ship that obviously is inferior in any fights, like Heavy Tanker. It just reinforces the idea that you are doing this for a RP reasons and not to just get hold of that capital you've always wanted. I would rule out all the cruisers and such since it immediately smells of wanting the big ship with an unusual ID for pvp reasons. It does not matter if you swear to God that you gonna use it only for RP when you are applying for special char, whereas a rare, big, inferior ship in will alleviate those suspicions straight away.
Have you given any thought at the Heavy Lifter? It's civilian and as such would not raise any eyebrows in the server. Rather I think it would spark interesting comments from people and provide you a chance to explain and RP instead of system wide comm "announcements" about your RP.
I probably will end up using the heavy tanker due it looking the closest to the part. The Lifter looks good at the back, but with the (clamps?) at the front it doesn't really give that light carrier feeling,even a jury rigged one.
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"If you're in a fair fight, you didn't plan it properly."\
Never go first,Never be last, and never volunteer for anything.