Hi Jack,
Welcome to this forum.
I don't know how many LM Limited R33 GTR Nissan made, here are some infos I found on Shin's Prospec motorsport site:
A limited edition called "LM-Limited" was released on 21st May 1996 as the anniversary model of Le Mans 24 Hours Race entry.
The main equipment feature an exclusive body colour "Champion Blue (#BT2)", front bumper with air duct, carbon fibre rear spoiler, and an exclusive sticker on the C pillars.
I am in So Cal also, are you in LA? I heard of your LM car from Sean and Hiro, but didn't know you have all 3 GTRs
As far as I know, Nissan never made a LM Limited R33 GTR with the N1 trim. Do you mean you put a N1 engine in your R33?
What color is your R32 and R34? Obviously your LM is blue

Are you the owner of that super clean white R32 V-spec II?
Jeff