The stock Bill Lawrence pickup dates the guitar from 1993-95. I'm a little surprised it has an Original Floyd Rose, since Jackson was using the Schaller Floyd as standard equipment at the time. The OFR didn't come in until 1996, when the Soloist was changed to its current specifications, with the Duncan pickups etc. Jackson's internal designation for the Schaller bridge was the "JT-590".
As for model number, they didn't use those before 1996. I believe they were calling your guitar the "Soloist Custom" at the time.
Here's the relevant page from the 1994-95 catalog:http://audiozone.dk/guitargallery/?cont ... Page18.jpg