Automated node opsec: timing correlation flaw

[CryptoVoyager24]

Timing attacks on automated nodes. need some advice.
Im using cloudflare tunnels for inbound webhooks. Node only uses tor for outbound.
But the timing is a dead giveaway. Webhook hits the server, tx hits the tor network right after. Anyone watching both sides can just link the timestamps and dox the real ip.
How do people add random delay to the broadcast? Hoping there is a native core setting for this. Really dont want to build a custom python script just to hold the tx. Thoughts?