I have a bpy Motor
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TTE420 is a KO4 body, will bolt right up but will require custom tune and might make more power than your motor is ready for unless you have at least put some rods in.
That turbo is too expensive not to get a custom tune and get the power you are paying for. Really a plain K04 with a good tune is max for a stock BPY motor. Once you go higher you leap to the need for a lot of expensive upgrades, forged internals, more fueling etc.
If your turbo has come apart there would be concern you have metal chunks around inside. Might be time to at least pull the pan etc. before you replace turbo.
If I were you, I would just get a new K04, they are fantastic.