The whole story is full of madness .
_ You use coinbase as a wallet . {extremely dangerous)
_ At once "i guess" you deposited 300k$ to your trading account then purchase 32 btc . {That's crazy}
_ You afford to send the 32 btc at once from coinbase to a private investment platform . {It should be a non-professional one, as no one is crazy to set automatically the refund of 32 btc}
_ You didn't mention that you contacted the private platform team about the issue, i think they are responsible about the consequences of their unprofessional system. {I can't find a reason why you don't mention the name of that platform}
OP , i expect you to have enough knowledge and cleverness to invest a big money in this risky way.
My advice to you can be resumed in this quote: {Good luck & Sorry for you big lost}
Most likely it should be the trading platform (the one that issued the refund) the one to pursue the situation with Coinbase, get the BTCs returned to them, and then send them to an address controlled by @LssPssn.