DO NOT put 350 thousand dollars on an exchange, period. Keep it either on a hardware wallet or a paper wallet. Anywhere else isn't going to be secure enough for $350K. When I say hardware wallet, I generally suggest NOT using a phone for obvious reasons, but your hard drive trezor or ledger or....
BASICALLY just MAKE SURE you don't have a single point of failure, as loss can happen and likely will. For large amounts like this, multi sig or 2FA in general for enhanced security where the keys are generated offline. Good luck. Gj cracking that old wallet. 350K damn, maybe you should have waited til BTC hit 100K b4 cracking it O_O haha