Wow, capturing an Igazra is an impressive feat! Good job on that! Not to mention the two Azdgari Warships and the UE Carrier. The Laziras are moderately difficult to capture, so that's not bad, either.
Your current ship is light enough it shouldn't have problems doing the mission. Same goes for your Azdgari Warships and Laziras. The problem is your UE Carrier escort. It takes three days to go through hyperspace whereas the rest of your fleet takes two days except for the Laziras taking one day. If you want to do that mission, you'll need to ditch the carrier. Sorry, but that's how it is.
Oh, don't worry about spelling things wrong. They're all strange spellings and it took me forever to memorize them. So, you're not the only one.