BEST way to get close to Mick Karn's tone?

I know their are older threads, but nothing recent.

I want to take up fretless, and to me Mick Karn's fretless playing is the the very best.

I don't have $6K to drop on a Wal (or 3 vintage basses to trade someone on here for one,) plus they are typically WAY heavier then I want anyhow).

I know the fretless Jazz basses won't do his tone for a fact.

What is my best way to get there on a relative budget ($1200 or less)? Fretless stingray? Get a fretless jazz and change pickups to humbuckers (which I know should be closer), fretless P? Ibanez? or something else.